~ Exponential Gamma Distribution Box ~ *4413# ~ Data forms for calculation of probabilities, quantiles, density and extreme value distributions for the exponential generalised gamma probability function (generalised Gumbel).

[1] ~ Parameters of the Exponential Gamma Distribution. ~ *44131#

Distribution parameters from mean value, standard deviation and and skewness, and vice versa.

[2] ~ Exponential Gamma Probability Integral. ~ *44132#

Calculation of cumulative and exceedance probability and density by given argument.

[3] ~ Inverse Exponential Gamma Probability Integral. ~ *44133#

Value of random variable by given cumulative or exceedance probability.

[4] ~ Extremes in Exponential Gamma Distributed Sample. ~ *44134#

Extreme values and extreme value distributions for the largest and smallest values in a sample of observations.

[5] ~ Characteristic Function of Exponentially Gamma Distribution. ~ *44135#

Characteristic function calculation for arbitrary parameter values.

[6] ~ Exponential Gamma Distribution - Extended Form. ~ *44136#

Complete form for parameters, moments, quantiles, density and extremes.

The distribution is two-sided, that is, it is defined from -infinity to +infinity. For this reason it may be a convenient alternative to the normal distribution in the case of skewed empirical data. It may also be an alternative to the Rice distribution as shown in Paragraph 4.2.2 (iii), call *4223*#. An example of application is worked out in Section 1.4.4 in connection with corrosion test data. Call *144*# for a quick look at the text.

Otherwise the distribution is particularly convenient for extreme value distribution purposes. General and special cases are discussed in Article 4.3. Call *43# for text or *43*1# for equations. Extreme value distribution for the exponential gamma distribution itself may be derived in terms of a new exponential gamma distribution as outlined in Paragraph 4.3.2 (v) (call *4325*# for text and *432*1# for equations). Applications to extreme value estimations appear in Section 1.2.4, Section 1.2.5 and Section 1.3.2. Call *124*#, *125*# or *132*# respectively.