#GAMMA CDF SOFTWARE#
If the software that is used does not have the incomplete gamma function but has gamma CDF (e.g. Calculating a CDF would require using a software that has the capability of evaluating incomplete gamma function (or evaluating an equivalent integral). The end result gives CDFs that are a function of the incomplete gamma function. The CDFs derived in the preceding section is a two-step approach – first raising a gamma distribution with scale parameter equals to 1 to a power and then adding a scale parameter. Computation of these CDFs would require the use of software that can evaluate incomplete gamma function.Īnother Way to Work with “Transformed” Gamma The inverse gamma distribution has two parameters with being the scale parameter and being shape parameter (the same two parameters in the base gamma distribution). The transformed gamma distribution and the inverse transformed gamma distribution are three-parameter distributions with being the shape parameter, being the scale parameter and being in the power to which the base gamma distribution is raised. “Transformed” Gamma CDF (with scale parameter) “Transformed” Gamma CDF (without scale parameter) Based on the two preceding sections, the following shows the CDFs of the three different cases. We still use the two-step approach – first deriving the CDF without the scale parameter and then add it at the end. Thus the CDFs are to be defined based on an integral or the incomplete gamma function, shown in the preceding section. The CDF of the “transformed” gamma distributions does not have a closed form. When the gamma distribution is raised to a power, the resulting CDF will be defined as a function of. The CDF can be evaluated numerically using software. Note that and are the gamma function and incomplete gamma function, respectively, defined as follows. The following is the expression of the gamma CDF.īy a change of variable, the CDF can be expressed as the following integral. Suppose that is a random variable that has a gamma distribution with shape parameter and scale parameter. Unlike the exponential distribution, the CDF of the gamma distribution does not have a closed form. The following derivation seeks to express the CDFs of the “transformed” variables in terms of the base CDF. Let, and be the probability density function (PDF), the cumulative distribution function (CDF) and the survival function of the random variable (the base distribution). The random variables, and are called transformed, inverse and inverse transformed, respectively. This post focuses on the distributions generated by raising a gamma distribution to a power. The previous post focuses on the example of raising an exponential distribution to a power. The previous post opens up a discussion on generating distributions by raising an existing distribution to a power.
0 kommentar(er)
