0
Still curious? Ask our experts.
Chat with our AI personalities
Coach
Steve
EzraAdd your answer:
Earn +20 pts
What is the use of the Gamma distribution?
It is very frequently used in statistics. First of all, multiplying a Chi-square random variable by a constant you obtain a Gamma random variable. So, for example, most estimates of variance obtained in inferential statistics have a Gamma distribution. The Gamma distribution can also be obtained by summing exponential random variables. So, the Gamma distribution pops out in models where the exponential distribution is used (e.g. reliability, credit risk). It is also used for Internet traffic modeling. See the StatLect entry (link below) for an introduction.
About the history of gamma distribution?
According to the links, Karl Pearson was first to formally introduce the gamma distribution. However, the symbol gamma for the gamma function, as a part of calculus, originated far earlier, by Legrenge (1752 to 1853). The beta and gamma functions are related. Please review the related links, particularly the second one from Wikipedia.
What is lambda in statistics?
Lamdba (like most Greek letters in statistics) usually denotes a parameter of a distribution (usually of Poisson, gamma or exponential distributions). This will specify the entire distribution and allow for numerical analysis of the probability generating, moment generating, probability density/mass, distribution and/or cumulant functions (along with all moments), as and where these are defined.
The most commonly used greek letters in statistics?
I'll give you some common Greek symbols used in statistical analyses. I can't tell you which is the most common one given the enormous task of reviewing every statistics book. The Greek mu for mean, sigma for variance and rho for correlation are probably the first ones that one encounters in statistical analyses. Also, beta for beta distribution, gamma for gamma distribution, chi for chi-squared distribution. Alpha and beta are common as distribution parameters. In derivations, delta is common for differences of variables. Tau is common for a time variable. You will find more information in the related link.
How gamma are members of the exponential family prove?
Think you've got this backwards. The exponential probability distribution is a gamma probability distribution only when the first parameter, k is set to 1. Consistent with the link below, if random variable X is distributed gamma(k,theta), then for gamma(1, theta), the random variable is distributed exponentially. The gamma function in the denominator is equal to 1 when k=1. The denominator will reduce to theta when k = 1. The first term will be X0 = 1. using t to represent theta, we have f(x,t) = 1/t*exp(-x/t) or we can substitute L = 1/t, and write an equivalent function: f(x;L) = L*exp(-L*x) for x > 0 See: http://en.wikipedia.org/wiki/Gamma_distribution [edit] To the untrained eye the question might seem backwards after a quick google search, yet qouting wikipedia lacks deeper insight in to the question: What the question is referring to is a class of functions that factor into the following form: f(y;theta) = s(y)t(theta)exp[a(y)b(theta)] = exp[a(y)b(theta) + c(theta) + d(y)] where a(y), d(y) are functions only reliant on y and where b(theta) and c(theta) are answers only reliant on theta, an unkown parameter. if a(y) = y, the distribution is said to be in "canonical form" and b(theta) is often called the "natural parameter" So taking the gamma density function, where alpha is a known shape parameter and the parameter of interest is beta, the scale parameter. The density function follows as: f(y;beta) = {(beta^alpha)*[y^(alpha - 1)]*exp[-y*beta]}/gamma(alpha) where gamma(alpha) is defined as (alpha - 1)! Hence the gamma-density can be factored as follows: f(y;beta) = {(beta^alpha)*[y^(alpha - 1)]*exp[-y*beta]}/gamma(alpha) =exp[alpha*log(beta) + (alpha-1)*log(y) - y*beta - log[gamma(alpha)] from the above expression, the canonical form follows if: a(y) = y b(theta) = -beta c(theta) = alpha*log(beta) d(y) = (alpha - 1)*log(y) - log[gamma(alpha)] which is sufficient to prove that gamma distributions are part of the exponential family.
Where can I read an introduction to the Gamma distribution?
Answer 1) Look up Gamma distribution in say Wikipedia or an on-line encyclopedia. This is not a simple subject.Answer 2) The Gamma distribution is essentially a generalization of the Chi-square distribution. Multiplying a Chi-square random variable by a positive constant you get a Gamma random variable. See also the introduction to the Gamma random variable on statlect.com (see link below).
What is the use of the Gamma distribution?
It is very frequently used in statistics. First of all, multiplying a Chi-square random variable by a constant you obtain a Gamma random variable. So, for example, most estimates of variance obtained in inferential statistics have a Gamma distribution. The Gamma distribution can also be obtained by summing exponential random variables. So, the Gamma distribution pops out in models where the exponential distribution is used (e.g. reliability, credit risk). It is also used for Internet traffic modeling. See the StatLect entry (link below) for an introduction.
What is the difference between Gamma distribution and Central limit theorem?
There is abig difference between them..gamma is a distribution but central limit theorm is just like a method or technique u use to approximate gamma to another distriution which is normal....stupid
About the history of gamma distribution?
According to the links, Karl Pearson was first to formally introduce the gamma distribution. However, the symbol gamma for the gamma function, as a part of calculus, originated far earlier, by Legrenge (1752 to 1853). The beta and gamma functions are related. Please review the related links, particularly the second one from Wikipedia.
What The cargo container improved distribution by introducing what methods into the shipping industry?
Standardization
What are examples of Gamma distribution in real life?
Waiting time until failure. Modelling insurance claims.
The cargo container improved distribution by introducing what methods into the shipping industry?
Standardization
How does a gamma scan work?
A gamma scan works by using a gamma camera to detect and capture the gamma radiation emitted by a radioactive substance inside the body. The camera creates images based on the distribution of the radiation, helping to identify any abnormalities or areas of interest, such as tumors or infections. The scan is non-invasive and provides detailed information about the structure and function of organs or tissues.
Advantage of performance appraisal?
It increase the motivation of the employee to perform well. Employee can understand their responsibility. Fair distribution of rewards.
What are the disadvantages of employee motivation?
Some disadvantages of employee motivation can include potential for burnout if not managed properly, unequal distribution of rewards leading to jealousy among team members, and potential for increased stress if performance expectations become unrealistic or unattainable.
What is lambda in statistics?
Lamdba (like most Greek letters in statistics) usually denotes a parameter of a distribution (usually of Poisson, gamma or exponential distributions). This will specify the entire distribution and allow for numerical analysis of the probability generating, moment generating, probability density/mass, distribution and/or cumulant functions (along with all moments), as and where these are defined.
What has the author Donald C Wold written?
Donald C. Wold has written: '[A NASA/University Joint Venture in Space Science]' -- subject(s): Cosmic ray showers, Density distribution, Diffuse radiation, Gamma ray observatory, Gamma ray telescopes, Radiation detectors
