How Opportunity Structures Affect Your Life

How Opportunity Structures Affect Your Life The term opportunity structure refers to the fact that the opportunities available to people in any given society or institution are shaped by the social organization and structure of that entity. Typically within a society or institution, there are certain opportunity structures that are considered traditional and legitimate, like achieving economic success by pursuing education in order to get a good job, or dedicating oneself to a form of art, craft, or performance in order to make a living in that field. These opportunity structures, and untraditional and illegitimate ones too,  provide sets of rules that one is supposed to follow in order to achieve cultural expectations of success. When traditional and legitimate opportunity structures fail to allow for success, people may pursue success via untraditional and illegitimate ones. Overview Opportunity structure is a term and theoretical concept developed by American sociologists Richard A. Cloward and Lloyd B. Ohlin, and presented in their book  Delinquency and Opportunity, published in 1960. Their work was inspired by and built upon sociologist Robert Mertons theory of deviance, and in particular, his structural strain theory. With this theory Merton suggested that a person experiences strain when the conditions of society do not allow one to attain the goals that the society socializes us to desire and work toward. For example, the goal of economic success is a common one in U.S. society, and the cultural expectation is that one would work hard to pursue education, and then work hard in a job or career in order to attain this. However, with an underfunded public education system, high cost of higher education and burdens of student loans, and an economy dominated by service sector jobs, U.S. society today fails to provide the majority of the population with adequat e, legitimate means to attain this kind of success. Cloward and Ohlin build on this theory with the concept of opportunity structures by pointing out there are a variety of pathways to success available in society. Some are traditional and legitimate, like education and career, but when those fail, a person is likely to pursue pathways provided by other kinds of opportunity structures. The conditions described above, of inadequate education and job availability, are elements that can serve to block a particular opportunity structure for certain segments of the population, like kids to attend underfunded and segregated public schools in poor districts, or young adults who have to work to support their families and thus do not have the time or money to attend college. Other social phenomena, like racism, classism, and sexism, among others, can block a structure for certain individuals, while still enabling others to find success through it. For example, white students might thrive in a particular classroom while black students do not, because teachers tend to underestimate the intelligence of black kids, and to punish them more harshly, both of which hinder their ability to succeed in the classroom. Relevance in Society Cloward and Ohlin use this theory to explain deviance by suggesting that when traditional and legitimate opportunity structures are blocked, people sometimes pursue success through others that are  considered nontraditional and illegitimate, like getting involved in a network of petty or major criminals in order to make money, or by pursuing grey and black market occupations like sex worker or drug dealer, among others.

Upcoming Changes to Interstate Driving Ages Open New Possibilities

Upcoming Changes to Interstate Driving Ages Open New Possibilities According to the American Trucking Association, the industry is currently facing a shortage of more than 30,000 drivers; many eligible drivers have been unable to secure cross-country or interstate routes because of insurance regulations that prohibit drivers younger than 21 from crossing state lines. Young drivers are eager to take more lucrative opportunities; insurance companies are often leery of trusting younger drivers for safety concerns, but according to Ken, Vice President of Spirit of CLD training services, â€Å"If they’re getting trained properly and you’re helping them grow up and realize †¦their responsibility and obligation†¦I don’t think age should matter.† He has even trained his daughter, Cheyenne, 18, to follow in his trucking footsteps- she’s looking forward to the potential jobs this change in regulation could open up for her.A bill coming before the Illinois legislature would allow bordering states to partner with one another in individual or group compacts that would allow 18-year-old drivers to cross between participating states. Detractors say a bigger pool of younger drivers would take jobs from more established operators- but the ATA’s deficit of drivers would seem to counter those concerns.

Architecture of any civilization Essay Example | Topics and Well Written Essays - 1000 words

Architecture of any civilization - Essay Example Architecture is an overt expression of the culture and beliefs of any society. Though the basic principle of manipulation of space in order to control the user of the space is universal, the subtleties may vary with the culture. A study of the various monuments belonging to different cultures that existed at different periods of history will help us understand this idea. We will first travel back to prehistoric times and take a glimpse at the 'Great Stone Tower of Jericho'. By doing so we will try to capture some of the beliefs, priorities and traditions of the people that lived in those times. This monumental structure was built between 8000 and 7000 BC. This tower makes Jericho the oldest known city in the world. The tower also proposes that the people who built it had settled there and were not nomadic food hunters. They also had an organized community in order to carry out such a task. The tower has only one entrance and steps made of well carved stones that lead to the summit. The summit is circular in shape. The structure controls the movement of the user by its single entrance and the steps that allow only up and down movement. The purpose of the tower seems to be defense which appears to be a very important consideration of that community. This could be the reason for building five feet thick walls and ditches around these towers. This shows that the people were in fear of a mighty foe that they had to keep out of their territory, and for the people that built this structure life must have revolved around military and other defense problems of their day. This structure thus gives us a picture of the life of the people in those times. Nothing can match the excellent example of the pyramids when it comes to architecture and space manipulation. The pyramids are also a primary source of information about the life and death beliefs and ceremonies of the people and the kings that ruled them. The primary function of these pyramids was to serve as funerary complexes to the pharaohs who were worshipped as gods. These gigantic monuments speak with the voice of the dead about the enchantment of the people of their times with the afterlife. The preserved body of the pharaoh with the provisions needed for his afterlife was kept in these pyramids. They also served as ceremonial cites and places of worship where the people worshipped the deceased king as God. To this day they stand as an architectural marvel. The size of these structures is massive and the question of how the huge stones were carried up as the building progressed is a mystery. Another interesting part of the pyramid was the Ben Ben which formed the capstone of the pyramid. This was made of shining material like gold or silver. The Ben Ben is believed to represent the rays of the sun. Egyptians worshipped and revered the sun god as the supreme provider of life on earth. The hieroglyphics on the pyramid also talks about the solar eclipse, and other planetary events, telling us how the Egyptians followed the happenings on the sky and related them to life here on earth. The Stepped Pyramid and mortuary precinct of Djoser, Saqqara, Egypt, was built between 2630-2611 BCE. It was built as a grandiose royal tomb. Such monuments represented eternal life after death and were designed to last for. A great amount of money and manpower was pumped in to build these. The shape of the pyramid with the slopes on the four sides

The Perspective of Moral law and Circumcision Essay

The Perspective of Moral law and Circumcision - Essay Example They are ones who do not consider Jesus as God instead believes that a Messiah will be the one to unite everyone towards the kingdom of God. Gentiles on the other hand are those people who are not seen as a descendant of Israel and at the same time people who do not see themselves as one, which often takes their right to worship God. However, they still do worship God based on His teachings told to them through different people chosen by God such as Moses. Now, after clearly setting enough light on what Gentiles and Jews were, it is now easier to know the difference between how each perceived moral law. The latter are those who obeyed the law based on their traditions rather than what God truly meant in His teachings. On the other hand, Gentiles are those who followed Jesus because they put importance in living under no other law but Christ’s (New International Version (NIV Bible) - Version Information - BibleGateway.com. (n.d.)). Thus, when it comes to the topic on circumcision in the olden days, each of them would have different purposes and attitude towards doing so. For the Jews, circumcision, which was one of the clearly stated teachings in the Old Testament was just an act they had to do to be able to avoid persecution from the people. Another reason why they do not really believe in circumcision being a holy and biblical act is because of the fact that even those that are circumcised sin. However, for Gentiles, circumcision is a whole different thing. Even when Gentiles are seen as those who do not have the law and not being the chosen people of God, they do things that are required by the law of God not only obeying by word but at the same time has the law written in their hearts (New International Version (NIV Bible) - Version Information - BibleGateway.com. (n.d.)). Thus, for them, circumcision is an act done to please God by not only getting circumcised but at the same time by observing the other laws and not just pick out the laws that might

Key Components in the Leisure and Recreation Industry Essay Example for Free

Key Components in the Leisure and Recreation Industry Essay Recreational activities fall into six key components, which in turn are divided into sectors. Some activities will fit into more than one category, and other activities are hard to put into any category, such as bridge clubs- are they a sport or a home based leisure activity ? The main components are: * Arts and Entertainment * Home-based Leisure * Countryside recreation * Catering * Heritage and visitor attractions * Sports and physical recreation Arts and Entertainment This is a huge industry that includes many sectors, they are: Arts The arts, apart from commercial cinema and theatre is a precarious industry where losses are easily incurred due to high costs and a very fragmented market. Sponsorship and grants play an important part in these. The public sector plays the most crucial part in funding arts. At the top is the Arts Council, which in 1999 gave out à ¯Ã‚ ¿Ã‚ ½188 million in grants. Much of this came from the National Lottery. Some of it was given out to Regional Arts Boards who then fund local projects. Much of the grant aid is given directly to organisations or individuals. The Arts Council is not the only national public sector organisation to be involved in the arts. One important group is The British Film Institute (BFI) which is responsible for supporting film makers, and the promotion of the British film industry. Local authorities play an important role as well. They employ arts development officers who promote the arts locally and will support local artists. Some larger authorities employ established artists in residence, who work in the area promoting their art and creating commissioned pieces. Local Authorities are major providers of galleries and performance space such as town hall stages or community theatres or even parish halls. In some cases, such as the Lyric Theatre at Hammersmith, London is a part owner of a commercial theatre. Voluntary sector groups also contribute to this sector. Many trusts exist to develop minority arts or provide for specialist audiences. For example, Wolf and Water in Devon is a drama trust dedicated to working with people with special needs. Entertainment Classified as entertainment are popular performing arts and spectacles. The voluntary sector is important here as nationwide participation in amateur dramatics and music is a popular pursuit. Public provision is also evident but has changed in recent years. Thirty years ago most town halls and civic entertainments programme of films, theatre and musicals. This has largely disappeared now and has been replaced by events programmes that are organised by various departments. For example, many sports centres will host travelling theatre and ballet companies such as the Royal Exchange Theatre Group, while arts officers will book in tourism exhibitions. In the streets and parks outside, groups are invited to put on events such as the hot-air balloon events in Bristols Parks. It is the private sector that monopolises entertainment. There is a flourishing small-business sector that includes pub entertainments and single artists such as party and street entertainers, but the bulk of the market is contained within three areas: 1.cinemas 2. Theatre 3. Stadia/arenas Cinema-was very popular in the first half of the 20th century. Then when colour televisions and video players appeared cinemas started to lose there appeal to the public. Cinema companies were not refurbishing their buildings, most of which were built in the 1930s, and were finding profit by selling them off as bingo halls. Some survived by aiming at niche markets(e.g. Corner House in Manchester). These art house cinemas show foreign films. The main market is for commercial English-language films. In the 1980s there was a major review of how films were presented. This resulted in multiplexes being invented. They are equipped with the following features: * Modern luxurious buildings with high-quality projection and sound * Multi screens to show move films than one * Easy access often at out-of-town centres * Good customer care The closest multiplex cinema around is the Warner Brothers Village in Longwell Green. This complex has all the features shown above Theatre-the London theatres are highly profitable with a city audience and a huge tourist market. Even then, they increasingly stick to a formula of musicals or familiar plays with big name actors. For example Chitty Chitty Bang Bang was shown at Londons Palindrome with Michael Ball starring in it. The package largely consists of touring West End shows, nostalgia and tribute bands, comedians and spectacles like circus and ice shows. The main London Theatre companies are: * Delfont Mackintosh Theatres * Ambassador Theatre Group * Really Useful Theatres * SFX (Apollo) Apollo leisure is the leading national chain Arenas and Stadia- these are large multi-purpose buildings for very large audiences. Arenas(indoor) for example are likely to put on conferences and trade exhibitions as well as concerts, while stadia(outdoor) are designed especially for sport. An example of a stadia is Ashton Gate home to Bristol City Football Club. Many arenas are owned by Local Authorities or development corporations. Good examples of this are the various halls and centres in Birmingham ,including the National Arena. Sports and physical recreation These activities can be grouped as follows: * Informal recreation(play, walking, gardening) * Competitive sport (football, tennis, golf) * Outdoor activities (sailing, climbing) * Health and fitness (jogging, yoga) Many activities can often be put into more than one category. For example, swimming in the sea is informal, swimming for a club is competitive, swimming in a conventional pool can be seen as health and fitness. Each component has a different profile in the type of facilities and services it produces. Informal physical recreation or exercise- this is the most popular activity nationally. Nobody knows the hours children spend playing or adults spend gardening. We pursue these activities because they are cheap, available and dont require a lot of skill. The enjoyment we get from them often depends on the environment we do them in. Competitive Sport-most people associate sport with the professional game. This means they are spectators, and it is the spectators money that underpins professional sport. Facilities were often run down to the extent that some were dangerous for crowds, e.g. Hillsborough 1989. Providers have found that profits increase when standards of customer care and corporate hospitality are improved. This has led to the building of a new generation of high-class stadia and race tracks and other facilities where the key services are: * Presentation of the core event * Merchandising * Catering * Safety and security Amateur sport is geared around participation and voluntary clubs. As land and buildings are expensive, many clubs use facilities provided by Local Authorities. Many outdoor sports clubs have their own facilities although there is an even greater number of players who use recreation grounds. There are about 78,000 pitches in the country. Thirty years ago amateur sport was largely centred on outdoor team games. Competitive sport means participation and developing skills and there is a sizeable industry for coaches and instructors. Despite its profile, competitive sport is on the decline and organisations like Sport England are concerned that as a nation we are losing our sporting skills and becoming less fit and healthy. For example, many governing bodies have big school-based programmes, and Local Authorities will run schemes in deprived areas where people cannot afford to play sport or go to health suites. Outdoor Activities-there are over a thousand centres in the UK which specialise in providing outdoor adventure holidays. Facility provision is also essential for outdoor sports, meaning the upkeep of the environment, and this is regulated by the organisations under the Countryside Agency umbrella, such as the Forestry Commission, Local Authorities or National Trust. For most participants activity in the natural world is occasional, and more time will be spent in training in built facilities such as pools or climbing walls. Profitable areas such as skiing, sailing, private sector companies are the main providers. Health and Fitness- there are now at least 2,500 private health and fitness clubs in the UK- it is a boom industry that many young people see as the exciting place to work in leisure. Private sector will increasingly dominate the market and eventually also manage and invest in public sector facilities on behalf of Local Authorities. The central product of these clubs is the fitness room consisting of cardiovascular equipment and perhaps free weights, and frequently areas with small pools, jacuzzis and saunas.. Heritage and visitor attractions The heritage industry concerns buildings and materials that have historical value. Thirty years ago these were largely stately homes, castles, ruins such as Stonehenge and battlefields. Heritage was often about how the rich and famous had lived or what they had collected, or about culture(e.g. Shakespeare). Now it has expanded to include a much wider interpretation of historical value. Whether the attraction is a theme park or museum, the organisers will do their best to employ all the techniques of facility management to look after the customer and make the product interesting. In a theme park the excitement of the rides is a key feature and bringing new and more exciting rides brings in more customers. The difference between a visitor attraction and a heritage site is that the latter involves considerable work behind the scenes which the public never sees. The most popular tourist attractions are: * Museums and galleries- British Museum * Theme parks- Blackpool Pleasure Beach * Historic houses and monuments- Tower of London * Wildlife parks and zoos- London Zoo Many heritage sites are owned by Trusts and limited companies that have been set up to manage individual sites, while many stately homes are owned and run by two big organisations: * English Heritage- is the national body responsible for the management, promotion and conservation of 400 archaeological sites and the historic environment * The National Trust- is a trust set up in 1895 to preserve places of historic interest or natural beauty. Its sites include a range from Paul McCartneys teenage home to stately homes like Waddesdon Manor Museums-are not usually run by the private sector, largely because of high costs. Many museums started life as private collections which were later donated to the nation or the local community. Libraries-apart from their lending their services which we will look at later, they are largely involved in the heritage sector. They have a back-room role of collecting important documents including maps, and making these available to the public. This is known as the records and archives service. Catering Leisure catering includes pubs and clubs, restaurants, cafes and takeaways. Its firmly placed in the private sector with some exceptions. A catering company provides a service according to the specification of the client and often under the clients name. Many leisure centres and theatres buy in service in this way. The catering sector has various components that make eating out an enjoyable experience: the provision of food and drink; entertainment, such as jazz at Pizza Express, games; and security in the form of door staff. Eating out is an increasingly important and available leisure experience. The fast-food business is booming with a growth rate of 30 per cent. This growth is at the expense of takeaways and cafes, and especially of pubs and clubs. Fast food tends to be run by chains that can make economies of scale by producing the same product in each outlet. Many breweries have followed this trend and operate chains like Harvester restaurants within their pubs. In contrast cafes, restaurants and takeaways tend to be run and owned by family businesses. Countryside recreation The countryside is the natural, national playground and one which is used by walkers, ramblers and those involved in more active outdoor activities. A survey in 1998 by the National Centre for Social Research showed that 1,427 million day visits to the countryside were made and a further 241 million to the coast. Like any leisure facility such usage will have an impact which in turn will lessen, and even threaten, the leisure experience itself. Organisations working in countryside recreation are therefore primarily stewards who maintain, manage and regulate the environment and also produce information and education. An important organisation funded by the Countryside Commission is the National Parks Authority. This is responsible for the regulation and interpretative service inside twelve National Parks, which are designated areas of significant natural beauty and wilderness. The Local Authority has a part to play in managing and regulating country parks. In many cases it also owns the land and will act as landlord to any tenants in the park, such as farmers. Home-based leisure This is cheap, easy and relaxing. The equipment most popularly used are: radios, videos, TV sets, gardening materials and home fitness machines is normally provided by the private sector. The main exceptions are the library lending services in the public sector. Except for broadcasting this component is retail based. As the internet is more widely used, shopping for leisure on the net is likely to increase. Free services like Tesco mean more people are using the net.

An Observation of Virgils Aeneid, Book II :: Virgil Aeneid Essays

An Observation of Virgil's Aeneid, Book II The Romans, unlike the Greeks were not gifted in abstract thought. They constructed no original system of philosophy, invented no major literary forms, and made no scientific discoveries. Yet, they excelled in the art of government and empire building, they created a workable world-state and developed skills in administration, law, and practical affairs. In the Punic Wars, the Roman republic defeated the Carthaginians in North Africa and Rome inherited the Pergamene Kingdom from the last of the Attalids in 133 B.C. Rome became heir to the legacy of the Hellenistic world of the Greeks. The Hellenistic period which lasted 300 years in is noted by the death of Alexander in 323 B.C. It is marked by its rich, sophisticated and diverse culture. Many Romans were eager to merge with this Greek culture in order to exhibit the dominance of their rule over conquered societies. This exhibition of dominance was the primary motivation of the Roman desire to possess fine works of Greek Art. Whereas, other Romans, were convinced that the pursuit of the assimilation of foreign cultures would only harm the republic. During this time, much social disintegration and unhindered individualism threatened political stability. However, the adoption of Greek art for Roman needs was very popular. An educated Roman was well versed in the history of Greek Art and was socially compelled to collect Greek art for personal embellishment. The modernization of the old Sanctuary of Fortuna Primigenia is an example of the new Roman attitude toward art and architecture as Greek artists migrated in vast numbers to the new capital of the world. Roman generals and their quest to establish Rome as the new unchallenged capital of the world justified the expense of replanning the old sanctuary. This accomplishment would bring them personal glory and uplift the majestic status of Roman people. Roman architecture benefited as the city's wealth grew as other leaders contributed to the expansion of new monuments. Lucias Cornelius Sculla, (82-78 B.C.) led the Romans is Social War and later became dictator and master of the city of Rome. He brought Corinthian columns form the temple of Olympian Zeus in Athens to renew the shrine of the Roman Jupiter in the capital. This act symbolized the transferal of spiritual power from the aristocracy of the Senate to autocratic leaders, and art began to be shaped by their preferences. This satisfied the Roman desire for grandiose architecture by being the model of Hellenistic majestic ornate style.

Analytical Essay – Lochie Leonard

Awkwardness, rudeness and moodiness are stereotypes which are used to represent teenagers. In his novel â€Å"Locke Leonard the Human Torpedo', Tim Wanton explores the emotional development of teenagers. In the novel he represents teenagers as reckless. This is achieved through Locale's inappropriate actions, rude behavior and his bad language. The novel displays teenagers as reckless through their inappropriate behavior.In the chapter ‘Getting Serious' Locke and Vicki are alone in her house and they engage n sexual activities disregarding the possible consequences. This is also shown later on in the book in the chapter ‘Ocean Beach' where they again act without thinking. The two chapters give the reader a clear example that teenagers can be reckless due to their inappropriate behavior. At school Locke displays rude behavior towards his teachers.In the chapter ‘Everybody's Favorite Spread' Locke is in class studying his least favorite subject, Math, and is rude to his teacher by omitting to call him sir (pap-18). Also in the chapter ‘True Torpedoing' Locke is in his woodwork class and once again displays dude behavior and insolence to his teacher by suggesting that the teacher ‘does his block (pap-31). This insulting comment could enrage an already hostile teacher even more and is therefore reckless.In the first two weeks Locke has already acquired a bad reputation for himself. Locale's rude behavior is very risky. Teenagers are represented as reckless due to their use of inappropriate or bad language. Locke has been influenced to use bad language after reading a book about sexual development. In the chapter ‘Everyone's Favorite Spread' Locke is being bullied. Whilst being bullied he retaliates by calling them ‘a bunch of yellow vulvas! (pap), which might provoke them to attack him, rather than trying to calm them down, which would be more sensible. Locale's use of language clearly represents teens as reckless. In this novel Tim Wanton represents teenagers as reckless because of their inappropriate actions, rude behavior and bad language. He has focused on emotional development in adolescents. While this is only one aspect of the challenges faced by teens, the author has represented common stereotypes in characters and their actions to describe teenagers.

Whole Foods Market SWOT

Whole Foods Market is one of the largest retailers of organic food products in the world. The company is successful because of its skilful growth strategy, huge product variety, and big profits. Whole Foods Market’s motto is â€Å"Whole Foods, Whole People, Whole Planet†, and this motto, as well as the core values, are very important for the company’s strategy and operating practices. However, the company does not execute the motto completely due to its poor international operations, which is one of the biggest weaknesses of Whole Foods Market. One of the opportunities of the company is the superiority in the market of high demand for the organic products. Increase in the competition in the market is one of the biggest threats for Whole Foods Market.Firm’s StrengthsWhole Foods Market grew from a local market to one of the largest organic product retailer around the world. By 2008, Whole Foods Market operated and owned 276 stores in the United States and in ternationally. The company’s expansion strategy consists mostly of acquisitions of other companies. One of the biggest and most important acquisitions was the acquisition of Wild Oats stores, which gave Whole Foods Market opportunity to operate with large scale stores and with less competition in that segment of market.The company offers a huge variety of products which includes: grocery, bakery, poultry and meat, seafood, deli, wines, cheese, and household products. The regular average size of a Whole Foods Market store is around 45,000 to 60,000 sq ft. In the bigger stores, which size up from 60,000 to 80,000 sq ft, they offer even a bigger variety of products and catering service. Example of this would be the Austin 78,000 sq ft store which included hundreds types of cheese, beers, wines, and seafood items.Whole Foods Market’s revenue was rapidly growing since the early 1990’s with an increase of 30%, and 20% increase since year 2000. By 2007 the company reco rded sales of around $6.6 billion. The revenue growth let the company to continue the expansions and acquisition of many more stores. Whole Foods Market acquired 134 stores since 1991 through 15 acquisitions.Firm’s WeaknessesWhole Foods Market has three stores in Canada, and six stores in the United Kingdom. The possession of such few stores internationally, the company is not able to arrive at the effect of economies of scale in distribution and purchasing. Because of weak operations internationally, the company’s prices are high, therefore lacking the company to compete with other international companies which have a larger operations scale.OpportunitiesWhole Foods Market is in a good market segment because of the rapid growth of demand for the organic products around the world. Consumers tend to slowly start preferring organic products to the regular packaged products. The organic market is growing very fast every year and everywhere around the world. Because of the increase in demand for organic products, which Whole Foods Market supplies, the company is going to experience an increase in sales and revenues.ThreatsSince the market for organic products is becoming more popular and growing, there are more players involved in the market. There are a lot of small companies and huge corporations who are entering the same market as Whole Foods Market, and some of them could be considered a respectful threat. Small supermarkets that supply organic foods, specialty supermarkets and restaurants are the small competitors. Wal-Mart on other hand is a potential strong competitor who announced in 2006 that the company is going to focus on organic segment, and is able to provide the consumers with low price organic products.Strenghts Skilful growth strategy Huge product variety Big profitsWeaknesses Poor international operationsOpportunity Market leadership in high demand marketThreats Increase of Competition

COLLEGE PAPER for All Academic Levels

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Maximum Likelihood Estimation Examples

Maximum Likelihood Estimation Examples Suppose that we have a random sample from a population of interest.  We may have a theoretical model for the way that the population is distributed.  However, there may be several population parameters of which we do not know the values.  Maximum likelihood estimation is one way to determine these unknown parameters.   The basic idea behind maximum likelihood estimation is that we determine the values of these unknown parameters.  We do this in such a way to maximize an associated joint probability density function or probability mass function.  We will see this in more detail in what follows.  Then we will calculate some examples of maximum likelihood estimation. Steps for Maximum Likelihood Estimation The above discussion can be summarized by the following steps: Start with a sample of independent random variables X1, X2, . . . Xn from a common distribution each with probability density function f(x;ÃŽ ¸1, . . .ÃŽ ¸k).  The thetas are unknown parameters.Since our sample is independent, the probability of obtaining the specific sample that we observe is found by multiplying our probabilities together.  This gives us a likelihood function L(ÃŽ ¸1, . . .ÃŽ ¸k)   f( x1 ;ÃŽ ¸1, . . .ÃŽ ¸k) f( x2 ;ÃŽ ¸1, . . .ÃŽ ¸k) . . .  f( xn ;ÃŽ ¸1, . . .ÃŽ ¸k) ÃŽ   f( xi ;ÃŽ ¸1, . . .ÃŽ ¸k).Next, we use Calculus to find the values of theta that maximize our likelihood function L.  More specifically, we differentiate the likelihood function L with respect to ÃŽ ¸ if there is a single parameter.  If there are multiple parameters we calculate partial derivatives of L with respect to each of the theta parameters.To continue the process of maximization, set the derivative of L (or partial derivatives) equal to zero and solve for theta.We can then use o ther techniques (such as a second derivative test) to verify that we have found a maximum for our likelihood function. Example Suppose we have a package of seeds, each of which has a constant probability p of success of germination.  We plant n of these and count the number of those that sprout.  Assume that each seed sprouts independently of the others.  How do we determine the maximum likelihood estimator of the parameter p? We begin by noting that each seed is modeled by a Bernoulli distribution with a success of p. We let X be either 0 or 1, and the probability mass function for a single seed is f( x ; p ) px (1 - p)1 - x.   Our sample consists of n  Ã‚  different Xi, each of with has a Bernoulli distribution.  The  seeds that sprout have Xi 1 and the seeds that fail to sprout have Xi 0.   The likelihood function is given by: L ( p ) ÃŽ   pxi (1 - p)1 - xi We see that it is possible to rewrite the likelihood function by using the laws of exponents.   L ( p )   pÃŽ £ xi (1 - p)n - ÃŽ £ xi Next we differentiate this function with respect to p.  We assume that the values for all of the Xi are known, and hence are constant.  To differentiate the likelihood function we need to use the product rule along with the power rule: L ( p )   ÃŽ £ xip-1 ÃŽ £ xi (1 - p)n - ÃŽ £ xi - (n - ÃŽ £ xi )pÃŽ £ xi (1 - p)n-1 - ÃŽ £ xi We rewrite some of the negative exponents and have: L ( p ) (1/p) ÃŽ £ xipÃŽ £ xi (1 - p)n - ÃŽ £ xi - 1/(1 - p) (n - ÃŽ £ xi )pÃŽ £ xi (1 - p)n - ÃŽ £ xi [(1/p) ÃŽ £ xi  - 1/(1 - p) (n - ÃŽ £ xi)]ipÃŽ £ xi (1 - p)n - ÃŽ £ xi Now, in order to continue the process of maximization, we set this derivative equal to zero and solve for p: 0 [(1/p) ÃŽ £ xi  - 1/(1 - p) (n - ÃŽ £ xi)]ipÃŽ £ xi (1 - p)n - ÃŽ £ xi Since p and (1- p) are nonzero we have that 0 (1/p) ÃŽ £ xi  - 1/(1 - p) (n - ÃŽ £ xi). Multiplying both sides of the equation by p(1- p) gives us: 0 (1 - p) ÃŽ £ xi  - p (n - ÃŽ £ xi). We expand the right hand side and see: 0   ÃŽ £ xi  - p ÃŽ £ xi  - p n pÃŽ £ xi   ÃŽ £ xi - p n. Thus ÃŽ £ xi p n and (1/n)ÃŽ £ xi   p.  This means that the maximum likelihood estimator of p is a sample mean.  More specifically this is the sample proportion of the seeds that germinated.  This is perfectly in line with what intuition would tell us.  In order to determine the proportion of seeds that will germinate, first consider a sample from the population of interest. Modifications to the Steps There are some modifications to the above list of steps.  For example, as we have seen above, is typically worthwhile to spend some time using some algebra to simplify the expression of the likelihood function.  The reason for this is to make the differentiation easier to carry out. Another change to the above list of steps is to consider natural logarithms. The maximum for the function L will occur at the same point as it will for the natural logarithm of L.  Thus maximizing ln L is equivalent to maximizing the function L. Many times, due to the presence of exponential functions in L, taking the natural logarithm of L will greatly simplify some of our work. Example We see how to use the natural logarithm by revisiting the example from above.  We begin with the likelihood function: L ( p )   pÃŽ £ xi (1 - p)n - ÃŽ £ xi . We then use our logarithm laws and see that: R( p ) ln L( p ) ÃŽ £ xi ln p (n - ÃŽ £ xi) ln(1 - p). We already see that the derivative is much easier to calculate: R( p ) (1/p)ÃŽ £ xi - 1/(1 - p)(n - ÃŽ £ xi) . Now, as before, we set this derivative equal to zero and multiply both sides by p (1 - p): 0 (1- p ) ÃŽ £ xi -  p(n - ÃŽ £ xi) . We solve for p and find the same result as before. The use of the natural logarithm of L(p) is helpful in another way.  It is much easier to calculate a second derivative of R(p) to verify that we truly do have a maximum at the point (1/n)ÃŽ £ xi   p. Example For another example, suppose that we have a random sample X1, X2, . . . Xn from a population that we are modelling with an exponential distribution.  The probability density function for one random variable is of the form f( x ) ÃŽ ¸-1 e -x/ÃŽ ¸ The likelihood function is given by the joint probability density function. This is a product of several of these density functions: L(ÃŽ ¸) ÃŽ   ÃŽ ¸-1 e -xi/ÃŽ ¸   ÃŽ ¸-n e -ÃŽ £ xi/ÃŽ ¸    Once again it is helpful to consider the natural logarithm of the likelihood function.  Differentiating this will require less work than differentiating the likelihood function: R(ÃŽ ¸) ln L(ÃŽ ¸) ln [ÃŽ ¸-n e -ÃŽ £ xi/ÃŽ ¸] We use our laws of logarithms and obtain: R(ÃŽ ¸) ln L(ÃŽ ¸) - n ln ÃŽ ¸Ã‚   -ÃŽ £xi/ÃŽ ¸ We differentiate with respect to ÃŽ ¸ and have: R(ÃŽ ¸)   - n / ÃŽ ¸Ã‚   ÃŽ £xi/ÃŽ ¸2 Set this derivative equal to zero and we see that: 0 - n / ÃŽ ¸Ã‚   ÃŽ £xi/ÃŽ ¸2. Multiply both sides by ÃŽ ¸2 and the result is: 0 - n ÃŽ ¸Ã‚   ÃŽ £xi. Now use algebra to solve for ÃŽ ¸: ÃŽ ¸ (1/n)ÃŽ £xi. We see from this that the sample mean is what maximizes the likelihood function.  The parameter ÃŽ ¸ to fit our model should simply be the mean of all of our observations. Connections There are other types of estimators.  One alternate type of estimation is called an unbiased estimator.  For this type, we must calculate the expected value of our statistic and determine if it matches a corresponding parameter.

Anything Essay Example | Topics and Well Written Essays - 250 words - 11

Anything - Essay Example House ownership grants one access to opportunities for families such as neighborhoods with good schools, jobs and public services. In order for one to get good housing the amount of money he is paid becomes a factor. This essay will examine the trends in housing and the financial position of an individual in details. There is a large gap in house ownership between different people which has continued to increase though barriers in homeownership for the minority groups were lifted long time ago. The current housing policy now targets minority homeownership with the specific intention of closing the gap in house ownership among different groups. The casual expansion of urban land which was traditionally professed as an significant way through which the poorest inhabitants of the urban centers got shelter. This has changed since most of the middle, and high-income households tend to buy land casually for housing. It is clear that those workers who are able to learn new working skills especially in technology will benefit from higher salaries. But on the other hand those who are used to carrying out routine jobs which can be handled by computers and robots will be competing with few jobs or will be pushed into low-skill jobs and hence it will be difficult for them to afford buying better houses (Tal ly 22). It is difficult for the middle-income people to purchase a house in the formal market. This is due to their low-income. This in turn forces them to construct low cost structures as their homes and expenses and can increase the budgets of the developer beyond the monetary capability of the scheme. The cost of land on the other hand, has increased greatly hence this leads to increase the housing gap. Those people who earn larger amount of money posses the ability to construct several houses, which they in turn they rent to the low-income earners at high costs In most parts of the country it evident