The fréchet stress-strength model
This paper deals with the determination of R = P[Y < X] when X and Y are two independent Fréchet distributions with different scale parameters and different shape parameters. Special cases when X and Y have the same shape parameter but having the different scale parameters, and when X and Y have the same scale parameter but having the different shape parameters, are also considered. The divergence problem of R is also discussed. Different methods to estimate R and Fréchet distribution parameters are studied, Maximum Likelihood estimator, Moments estimator, Regression estimator, Percentile estimator , least square estimator and L-moments estimator. An empirical study was conducted to support the theoretical aspect.
Keywords: Fréchet Distributions, Percentile Estimator, L-Moments Estimator, Maximum Likelihood Estimator, Stress- Strength.
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