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We present a generalized version of the univariate change-of-variable technique for transforming continuous random variables. Extending a theorem from Casella and Berger 3] for many{to{1 transformations, we consider more general univari-ate transformations. Speciically, the transformation can range from 1{to{1 to many{to{1 on various subsets of the support(More)
We present an algorithm for computing the cumulative distribution function of the Kolmogorov{ Smirnov test statistic D n in the all-parameters-known case. Birnbaum (1952) gives an n-fold integral for the CDF of the test statistic which yields a function deened in a piecewise fashion, where each piece is a polynomial of degree n. Unfortunately, it is diicult(More)
We present an algorithm for computing the probability density function of the product of two independent random variables, along with an an implementation of the algorithm in a computer algebra system. We combine this algorithm with earlier work on transformations of random variables to create an automated algorithm for convolutions of random variables.(More)
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A method to produce new families of probability distributions is presented based on the incomplete gamma function ratio. The distributions distributions produced also can include a number of popular univariate survival distributions, including the gamma, chi-square, exponential, and half-normal. Examples that demonstrate the generation of new distributions(More)
A variation of maximum likelihood estimation (MLE) of parameters that uses probability density functions of order statistic is presented. Results of this method are compared with traditional maximum likelihood estimation for complete and right-censored samples in a life test. Further, while the concept can be applied to most types of censored data sets,(More)
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