The fréchet stress-strength model - Abid, Salah (International Journal of Applied Mathematical Research, 2014)
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.