Journal of Data Science

This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.

In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.

We introduce a new family of distributions namely inverse truncated discrete Linnik G family of distributions. This family is a generalization of inverse Marshall-Olkin family of distributions, inverse family of distributions generated through truncated negative binomial distribution and inverse family of distributions generated through truncated discrete Mittag-Leffler distribution. A particular member of the family, inverse truncated negative binomial Weibull distribution is studied in detail. The shape properties of the probability density function and hazard rate, model identifiability, moments, median, mean deviation, entropy, distribution of order statistics, stochastic ordering property, mean residual life function and stress-strength properties of the new generalized inverse Weibull distribution are studied. The unknown parameters of the distribution are estimated using maximum likelihood method, product spacing method and least square method. The existence and uniqueness of the maximum likelihood estimates are proved. Simulation is carried out to illustrate the performance of maximum likelihood estimates of model parameters. An AR(1) minification model with this distribution as marginal is developed. The inverse truncated negative binomial Weibull distribution is fitted to a real data set and it is shown that the distribution is more appropriate for modeling in comparison with some other competitive models.