Statistical Inference for Multiply Truncated Power Series Distributions
STANFORD UNIV CA DEPT OF STATISTICS
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Convolutions of one-parameter power series distributions PSD truncated on the left at several known or unknown points are studied via exponential generating functions. The special cases of the logarithmic series, the Poisson and the binomial and negative binomial distributions lead to multiparameter Stirling numbers of the first and second type and C-numbers respectively. Minimum variance unbiased estimators are found for certain functions of the parameters, including the probability functions themselves. Some conditional distribution properties are given and it is indicated how they can be used in confidence interval estimation of the reliability of multicomponent attribute failure models.
- Statistics and Probability