COMPOSITION AND DECOMPOSITION OF BOUNDED VARIATES WITH SPECIAL REFERENCE TO THE GAMMA AND THE WEIBULL DISTRIBUTIONS.
Technical rept. Feb 64-Feb 65,
WEIBULL (WALODDI) LAUSANNE (SWITZERLAND)
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The algebra published in Technical Report No. ASD-TDR 63-63 has been further developed, and its use has been illustrated by some worked examples. After some modifications of the notations, the differentiation and integration of stochastics, including the variates as a special case, have been more thoroughly examined, in particular with respect to the concept of broken derivatives and integrals. A generalized distribution function has been set up. By proper specification of its two shape parameters, it can be brought to reproduce the density functions of the Exponential, Gamma, Pearson Type III, Chi-square, Rayleigh, Weibull, and some more distributions of practical importance. This general function has been expanded in a power series which is transformed in a series, called the integral series. Based on these formulae, rules for summation and multiplication of independent variates are presented and applied to some distributions. Inverse addenda for various variates have been developed and used for decomposition of sums of Gamma and Weibull variates. Author
- Statistics and Probability