A FORTRAN program for fitting Weibull distribution and generating samples

Abstract A computer program has been developed to estimate the parameters of the two-parameter Weibull distribution describing a given data set and to generate random numbers following a given Weibull distribution. The Weibull distribution parameters, namely Weibull modulus and scale parameter, are estimated using two methods: (i) linear regression after logarithmic transformation of the data and (ii) maximum-likelihood estimator. The cumulative distribution function (i.e. probability of failure of a specimen if the data set characterize strength of a component or probability of drought if the data represent water level, etc.) has been estimated using the order statistics. Both the Weibull modulus and scale parameter are necessary to generate random numbers with a specified Weibull distribution. Two example problems using published data sets are used to verify the code. Values of Weibull distribution parameters, estimated using this code, match published solutions obtained graphically. Parameters estimated from one of the example problems are used to generate a set of random numbers. Descriptive statistics and Weibull parameters estimated from the generated data match well with those obtained from the original data.