A new family of distributions to analyze lifetime data

Journal of Modern Applied Statistical Methods, 2020

In lifetime data, the hazard function is a common technique for describing the characteristics of lifetime distribution. Monotone increasing or decreasing, and unimodal are relatively simple hazard function shapes, which can be modeled by many parametric lifetime distributions. However, fewer distributions are capable of modeling diverse and more complicated shapes such as N-shaped, reflected N-shaped, W-shaped, and M-shaped hazard rate functions. A generalized family of lifetime distributions, the uniform-R{generalized lambda} (U-R{GL}) are introduced and the corresponding survival models are derived, and applied to two lifetime data sets. The survival model is applied to a right censored lifetime data set.

Model Assisted Statistics and Applications, 2019

In this paper it is introduced a new two-parameter discrete distribution derived from the continuous Sushila distribution (Shanker et al., 2013). Its mathematical properties and estimation procedures for the parameters of the proposed model are presented assuming complete and right-censored data. This new model, in the same way as the continuous Sushila distribution, has the discrete Lindley distribution as a special case. An extensive simulation study is carried out to examine the bias and the roots of the mean squared errors for the maximum likelihood estimators as well the moments and Bayesian estimators of the proposed model parameters. Some examples using simulated data and real datasets are considered to show that the new proposed model performs at least as good as its particular case and some other traditional discrete models as the Poisson and geometric distributions.

In this work the analysis of interval-censored data, with Weibull distribution as the underlying lifetime distribution has been considered. It is assumed that censoring mechanism is independent and non-informative. As expected, the maximum likelihood estimators cannot be obtained in closed form. In our simulation experiments it is observed that the Newton-Raphson method may not converge many times. An expectation maximization algorithm has been suggested to compute the maximum likelihood estimators, and it converges almost all the times. The Bayes estimates of the unknown parameters under gamma priors are considered. If the shape parameter is known, the Bayes estimate of the scale parameter can be obtained in explicit form. When both the parameters are unknown, the Bayes estimators cannot be obtained in explicit form. Lindley's approximation, importance sampling procedures and Metropolis Hastings algorithm are used to compute the Bayes estimates. Highest posterior density credible intervals of the unknown parameter are obtained using importance sampling technique. Small simulation experiments are conducted to investigate the finite sample performance of the proposed estimators, and the analysis of two data sets; one simulated and one real life, have been provided for illustrative purposes.

IJMAO, 2020

The paper introduces a new distribution called the Lomax-Weibull distribution using the competing risk approach of constructing lifetime distributions. Some structural and mathematical properties of the proposed lifetime distribution are considered. Parameter estimation of the Lomax Weibull distribution is obtained using maximum likelihood estimation. The applicability and exibility of the new distribution in lifetime analysis is illustrated with the aid of two real life examples.

Biostatistics and Biometrics Open Access Journal, 2018

In this paper, we proposed a new distribution to lifetime data with two parameters, the proposed distribution have increasing, decreasing and unimodal failure rates function. Some mathematical properties of the new distribution, including hazard function, moments, Estimation of Reliability, distribution of the order statistics and observed information matrix were presented. To estimate the model parameters, the Maximum Likelihood Estimate (MLE) technique was utilized. Then, one real data set were applied to show the significance and flexibility of the new distribution.

2014

The Weibull distribution is a popular and widely used distribution in reliability and in lifetime data analysis. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. Many modifications of the Weibull distribution have achieved the above purpose. On the other hand, the number of parameters has increased, the forms of the survival and hazard functions have become more complicated and the estimation problems have risen.This thesis provides an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution, which could serve as an important reference and encourage further modifications of the Weibull distribution. Four different modifications of the Weibull distribution are proposed to address some of the above problems using different techniques. First model, with five parameters, is constructed by considering a two-component serial system with one component following a Weibull...

Journal of the Indian Society for Probability and Statistics, 2020

The present paper introduces a class of distributions with quadratic hazard quantile function. We study various distributional properties and reliability characteristics of the proposed model. The proposed class of distributions aims to represent the nonmonotone behaviours of hazard quantile function. Characterizations of the model are presented and method of least square is employed to estimate parameters of the class of distributions. Finally, we illustrate the usefulness of the proposed model through real data sets.

Model Assisted Statistics and Applications, 2019

We study some mathematical properties of a new generator of continuous distributions with one additional shape parameter named the Marshall-Olkin extended-G (MOE-G) family. We propose a new distribution called the MOE-Flexible Weibull and obtain some of its structural properties. Further, we construct a regression model based on this distribution with two systematic components that can be applied to real lifetime data. We estimate its model parameters by maximum likelihood. We present a diagnostic analysis based on global influence and deviance residuals. Two real data sets are used to illustrate the potentiality of the proposed models.

Lifetime Data Analysis, 2006

A simple competing risk distribution as a possible alternative to the Weibull distribution in lifetime analysis is proposed. This distribution corresponds to the minimum between exponential and Weibull distributions. Our motivation is to take account of both accidental and aging failures in lifetime data analysis. First, the main characteristics of this distribution are presented. Then, the estimation of its parameters

Unilag Journal of Mathematics and Applications, 2021

In this article, Weibull link function initiated by Jones (2004) and extended Pranav distribution written by Uwaeme et al. (2018) are convolute to introduced Weibull-extended Pranav distribution using the idea of Tahir et al. (2016). The motivation is to develop a robust and flexible distribution that will have better fit to any skewed data set. Different properties of the proposed distribution are obtained. Estimation of model parameters with the method of maximum likelihood estimates are presented. Then, the new distribution is compared with some existing distributions by illustrating two different life time data sets. Hence, the results through estimation and goodness of fit criteria reveal that Weibull-extended Pranav distribution has better fit to the data sets than other distributions considered in the study.