A NEW FRÉCHET-G FAMILY OF CONTINUOUS PROBABILITY DISTRIBUTIONS: SPECIAL MODELS, PROPERTIES, SIMULATION AND APPLICATIONS

Abstract

This article derived a new family of continuous probability distributions known as New Frѐchet-G family of distributions. The study presents expansion and linear representation of the CDF and CDF of the new Frѐchet-G (NFr-G) family of distribution. The structural properties of the proposed family of distribution, such as quantile function, moment, moment generating function, characteristic function, reliability analysis and order statistics were derived. The parameters of the new family have been estimated using the method of maximum likelihood estimation. Four special models have been derived and discussed from the new Frѐchet-G family. The shapes of their densities and CDFs of the special models for some chosen parameter values were also discussed. The plots of the PDFs of the special models revealed that the NFr-G family will generate distributions with different shapes which is an indication that the proposed family is skewed and flexible. Monte Carlo simulation study was conducted to check the stability of the parameters of the proposed family through the NFrExD and the results revealed that the estimators of the parameters are consistent. The performance of the proposed family was assessed via the NFrExD by some applications of the model to real life data sets.