Abstract
Cumulative distribution function of the variable Y=(U+c)/(Z/2ν)) is given. Here U and Z are independent random variables, U has the exponential distribution (1.1) with θ=0, σ=1, Z has the distribution χ2 (2ν) and c is a real quantity. The variable Y with U and Z given by (2.2) and (2.3) is used for inference about the parametric functions ϕ=θ−kσ of a two-parameter exponential distribution (1.1) with k or ϕ known. Special cases of ϕ or k are: the parameter θ, the Pth quantile Xp, the mean θ+σ and the value of the cumulative distribution function or of the reliability function at given point a. Also one-sided tolerance limits for a two-parameter exponential distribution can be derived from the distribution of the variable Y. The results are also applied to the Pareto distribution.
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