A New Two-Parameter Burr-Hatke Distribution: Properties and Bayesian and Non-Bayesian Inference with Applications

This article introduces a two-parameter flexible extension of the Burr-Hatke distribution using the inverse-power transformation. The failure rate of the new distribution can be an increasing shape, a decreasing shape, or an upside-down bathtub shape. Some of its mathematical properties are calculated. Ten estimation methods, including classical and Bayesian techniques, are discussed to estimate the model parameters. The Bayes estimators for the unknown parameters, based on the squared error, general entropy, and linear exponential loss functions, are provided. The ranking and behavior of these methods are assessed by simulation results with their partial and overall ranks. Finally, the flexibility of the proposed distribution is illustrated empirically using two real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, Fréchet, gamma, exponential, inverse log-logistic, inverse weighted Lindley, inverse Pareto, inverse Nakagami-M, and Burr-Hatke distributions.

Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions.

APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS

In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.

An α-Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data

Modeling environmental data plays a crucial role in explaining environmental phenomena. In some cases, well-known distributions, e.g., Weibull, inverse Weibull, and Gumbel distributions, cannot model environmental events adequately. Therefore, many authors tried to find new statistical distributions to represent environmental phenomena more accurately. In this paper, an α-monotone generalized log-Moyal (α-GlogM) distribution is introduced and some statistical properties such as cumulative distribution function, hazard rate function (hrf), scale-mixture representation, and moments are derived. The hrf of the α-GlogM distribution can form a variety of shapes including the bathtub shape. The α-GlogM distribution converges to generalized half-normal (GHN) and inverse GHN distributions. It reduces to slash GHN and α-monotone inverse GHN distributions for certain parameter settings. Environmental data sets are used to show implementations of the α-GlogM distribution and also to compare its modeling performance with its rivals. The comparisons are carried out using well-known information criteria and goodness-of-fit statistics. The comparison results show that the α-GlogM distribution is preferable over its rivals in terms of the modeling capability.

The Extended Log-Logistic Distribution: Inference and Actuarial Applications

Actuaries are interested in modeling actuarial data using loss models that can be adopted to describe risk exposure. This paper introduces a new flexible extension of the log-logistic distribution, called the extended log-logistic (Ex-LL) distribution, to model heavy-tailed insurance losses data. The Ex-LL hazard function exhibits an upside-down bathtub shape, an increasing shape, a J shape, a decreasing shape, and a reversed-J shape. We derived five important risk measures based on the Ex-LL distribution. The Ex-LL parameters were estimated using different estimation methods, and their performances were assessed using simulation results. Finally, the performance of the Ex-LL distribution was explored using two types of real data from the engineering and insurance sciences. The analyzed data illustrated that the Ex-LL distribution provided an adequate fit compared to other competing distributions such as the log-logistic, alpha-power log-logistic, transmuted log-logistic, generalized log-logistic, Marshall–Olkin log-logistic, inverse log-logistic, and Weibull generalized log-logistic distributions.

Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

The extended Weibull–Fréchet distribution: properties, inference, and applications in medicine and engineering

<abstract><p>In this paper, a flexible version of the Fréchet distribution called the extended Weibull–Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical properties of the EWFr distribution are explored. The EWFr parameters are estimated using several frequentist estimation approaches. The performance of these methods is addressed using detailed simulations. Furthermore, the best approach for estimating the EWFr parameters is determined based on partial and overall ranks. Finally, the performance of the EWFr distribution is studied using two real-life datasets from the medicine and engineering sciences. The EWFr distribution provides a superior fit over other competing Fréchet distributions such as the exponentiated-Fréchet, beta-Fréchet, Lomax–Fréchet, and Kumaraswamy Marshall–Olkin Fréchet.</p></abstract>

Inverse Power Akash Probability Distribution with Applications

This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-tailed data than Akash, inverse Akash and power Akash distributions respectively.