Selecting among Probability Distributions Used in Reliability

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Abstract
A method is given for selecting the member of a collection of families of distributions that best fits a set of observations. This method requires a noncensored set of observations. The families considered include the exponential, gamma, Weibull, and lognormal. A selection statistic is proposed that is essentially the value of the density function of a scale transformation maximal invariant. Some properties of the selection procedures based on these statistics are stated, and results of a simulation study are reported. A set of time-to-failure data from a textile experiment is used as an example to illustrate the procedure, which is implemented by a computer program.

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