Modeling Lifetime Data Research Articles

Transmuted Burr Type X Distribution with Covariates Regression Modeling to Analyze Reliability Data

SYNOPTIC ABSTRACTThis article investigates the potential usefulness of the three-parameter transmuted Burr type X (TBX) distribution for modeling reliability data, and explore its structural properties using simulation. Explicit expressions are derived for moments, incomplete moments, entropies, and mean deviation. The method of maximum likelihood is used for estimating the model parameters. We conduct Monte Carlo simulations, which are used to examine the relative performance of the estimators using MLE in terms of bias and mean square errors. A location-scale regression model based on the log-TBX distribution is proposed for modeling lifetime data. Use of this family of distributions is illustrated for fatigue fracture data and multiple myeloma patient’s data.

Destructive cure rate models under proportional odds and associated likelihood inference

In this work, we introduce a flexible destructive cure rate model for lifetime data. We assume the number of competing causes of the event of interest to follow the Weighted Poisson distribution (including length-biased Poisson, negative binomial, and exponentially weighted Poisson [EWP]) and the lifetimes of the noncured individuals to follow a proportional odds survival model. The baseline odds distribution is considered to be either Weibull or log-logistic distribution. A damage distribution is introduced due to the fact that some of the competing causes may not remain active following treatment. The statistical inference is developed for this model under right-censored data. The maximum likelihood estimation of the model parameters is then developed with the full usage of expectation–maximization method. Model discrimination between destructive negative binomial cure rate model and destructive EWP cure rate model is carried out by likelihood-based criteria through AIC and BIC. An extensive simulation study is performed to evaluate the performance of all the models and inferential methods developed here. A real data example on cutaneous melanoma is analyzed for illustrative purpose.

Exponentiated Inverse Rayleigh Distribution and an Application to Coating Weights of Iron Sheets Data

This article aims to introduce a generalization of the inverse Rayleigh distribution known as exponentiated inverse Rayleigh distribution (EIRD) which extends a more flexible distribution for modeling life data. Some statistical properties of the EIRD are investigated, such as mode, quantiles, moments, reliability, and hazard function. We describe different methods of parametric estimations of EIRD discussed by using maximum likelihood estimators, percentile based estimators, least squares estimators, and weighted least squares estimators and compare those estimates using extensive numerical simulations. The performances of the proposed methods of estimation are compared by Monte Carlo simulations for both small and large samples. To illustrate these methods in a practical application, a data analysis of real-world coating weights of iron sheets is obtained from the ALAF industry, Tanzania, during January-March, 2018. ALAF industry uses aluminum-zinc galvanization technology in the coating process. This application identifies the EIRD as a better model than other well-known distributions in modeling lifetime data.

Zero-adjusted defective regression models for modeling lifetime data

ABSTRACTIn this paper, we introduce a defective regression model for survival data modeling with a proportion of early failures or zero-adjusted. Our approach enables us to accommodate three types of units, that is, patients with ‘zero’ survival times (early failures) and those who are susceptible or not susceptible to the event of interest. Defective distributions are obtained from standard distributions by changing the domain of the parameters of the latter in such a way that their survival functions are limited to . We consider the Gompertz and inverse Gaussian defective distributions, which allow modeling of data containing a cure fraction. Parameter estimation is performed by maximum likelihood estimation, and Monte Carlo simulation studies are conducted to evaluate the performance of the proposed models. We illustrate the practical relevance of the proposed models on two real data sets. The first is from a study of occlusion of endoscopic stenting in patients with pancreatic cancer performed at A.C.Camargo Cancer Center, and the other is from a study on insulin use in pregnant women diagnosed with gestational diabetes performed at São Paulo University Medical School. Both studies were performed in São Paulo, Brazil.

Modeling lifetime data with the odd generalized exponentiated inverse Lomax distribution

Modeling lifetime data with the odd generalized exponentiated inverse Lomax distribution

Modeling Lifetime Data with the Odd Generalized Exponentiated Inverse Lomax Distribution

Modeling Lifetime Data with the Odd Generalized Exponentiated Inverse Lomax Distribution

On Type II Half Logistic Weibull Distribution with Applications

In recent years, several of new improved and extended probability distributions have been discovered from the current distributions to facilitate their applications in many fields. A new three-parameter distribution, the so called the T ype II half logistic Weibull (TIIHLW), is introduced for modeling lifetime data. Some mathematical properties of the TIIHLW distribution are provided. Explicit expressions for the moments, probability weighted moments, quantile function, order statistics and Renyi entropy are investigated. Maximum likelihood estimation technique is employed to estimate the model parameters and simulation issues are presented. In addition, the superiority of the subject distribution is illustrated with an application to two real data sets. Indeed, the TIIHLW model yields a better fit to these data than the beta Weibull, Mcdonald Weibull and exponentiated Weibull distributions. Keywords : Type II half logistic-G class; Weibull distribution, Order statistics; Maximum likelihood method. DOI : 10.7176/MTM/9-1-05

Kumaraswamy log-logistic Weibull distribution: model, theory and application to lifetime and survival data

We develop the new Kumaraswamy Log-Logistic Weibull (KLLoGW) distribution by combining the Kumaraswamy and Log-logistic Weibull distributions. This new model is flexible for modelling lifetime data. Some statistical properties including quantile function, hazard rate function, moments and conditional moments are presented. Model parameters are estimated via the method of maximum likelihood and a Monte Carlo simulation study conducted to assess the accuracy of the estimates. Finally, the model is applied to a real dataset.

Logarithm Transformed Fr´echet Distribution : Properties and Estimation

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr\'{e}chet (ALTF) distribution is introduced which offers a more flexible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R\'{e}nyi and $\delta$-entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.

LINDLEY PARETO DISTRIBUTION

Abstract In this paper, we introduce a new Lindley Pareto distribution, which offers a more flexible model for modelling lifetime data. Some of its mathematical properties like density function, cumulative distribution, mode, mean, variance, and Shannon entropy are established. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators of the unknown parameters. Three real data sets are fitted to illustrate the importance and the flexibility of the proposed distribution.

Modeling lifetime data with Weibull-Lindley distribution

Modeling lifetime data with Weibull-Lindley distribution

A flexible bimodal model with long-term survivors and different regression structures

The cure fraction models are useful to model lifetime data with long-term survivors. In this paper, we introduce a flexible cure rate survival model where the model parameters are related to covariates in different regression structures. The regression model allows to model jointly the location, scale and shape effects. The maximum likelihood method is employed to estimate the model parameters. We provide Monte Carlo simulation experiments to verify the performance of the maximum likelihood estimates for different sample sizes and cure rate percentages. Furthermore, some diagnostic measures to assess departures from model assumptions as well as to detect outlying observations are also considered. Finally, applications to real data are presented to show the usefulness of the new cure rate model.

A New Generalized Transmuted Inverse Exponential Distribution: Properties and Application


 
 
 
 In this study, we proposed a new generalised transmuted inverse exponential distribution with three parameters and have transmuted inverse exponential and inverse exponential distributions as sub models. The hazard function of the distribution is nonmonotonic, unimodal and inverted bathtub shaped making it suitable for modelling lifetime data. We derived the moment, moment generating function, quantile function, maximum likelihood estimates of the parameters, Renyi entropy and order statistics of the distribution. A real life data set is used to illustrate the usefulness of the proposed model. 
 
 
 
 

Generalized linear exponential geometric distributions and its applications

This paper introduces an extension of the generalized linear exponential geometric distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, among others. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. • A new extended model of GLEG is introduced and studied. • Several reliability and statistical properties are obtained. • The unknown parameters of the new model are estimated. • Some applications in the context of statistics and reliability are provided. • The obtained results are validated using a real data set and it is shown that the new model provides a better fit than some other known distributions.

A Hierarchical Model for Heterogenous Reliability Field Data

ABSTRACTWhen analyzing field data on consumer products, model-based approaches to inference require a model with sufficient flexibility to account for multiple kinds of failures. The causes of failure, while not interesting to the consumer per se, can lead to various observed lifetime distributions. Because of this, standard lifetime models, such as using a single Weibull or lognormal distribution, may be inadequate. Usually cause-of-failure information will not be available to the consumer and thus traditional competing risk analyses cannot be performed. Furthermore, when the information carried by lifetime data are limited by sample size, censoring, and truncation, estimates can be unstable and suffer from imprecision. These limitations are typical, for example, lifetime data for high-reliability products will naturally tend to be right-censored. In this article, we present a method for joint estimation of multiple lifetime distributions based on the generalized limited failure population (GLFP) model. This five-parameter model for lifetime data accommodates lifetime distributions with multiple failure modes: early failures (sometimes referred to in the literature as “infant mortality”) and failures due to wearout. We fit the GLFP model to a heterogenous population of devices using a hierarchical modeling approach. Borrowing strength across subpopulations, our method enables estimation with uncertainty of lifetime distributions even in cases where the number of model parameters is larger than the number of observed failures. Moreover, using this Bayesian method, comparison of different product brands across the heterogenous population is straightforward because estimation of arbitrary functionals is easy using draws from the joint posterior distribution of the model parameters. Potential applications include assessment and comparison of reliability to inform purchasing decisions. Supplementary materials for this article are available online.

Proportional Odds under Conway-Maxwell-Poisson Cure Rate Model and Associated Likelihood Inference

Cure rate models are useful while modelling lifetime data involving long time survivors. In this work, we discuss a flexible cure rate model by assuming the number of competing causes for the event of interest to follow the Conway-Maxwell Poisson distribution and the lifetimes of the non-cured individuals to follow a proportional odds model. The baseline distribution is considered to be either Weibull or log-logistic distribution. Under right censoring, we develop the maximum likelihood estimators using EM algorithm. Model discrimination among some well-known special cases are discussed under both likelihood- and information-based criteria. An extensive simulation study is carried out to examine the performance of the proposed model and the inferential methods. Finally, a cutaneous melanoma dataset is analyzed for illustrative purpose.

Statistical Inference for the power Lindley model based on record values and inter-record times

A new generalization of the Lindley distribution, called the power Lindley distribution was proposed by Ghitany et al., (2013), which offers a more flexible distribution for modeling lifetime data, such as in reliability. They studied classical inferences for the model based on complete data sets. However, we may deal with record breaking data sets in which only values smaller (or larger) than the current extreme value are reported. In this paper, by using record values and inter-record times, we develop inference procedures for the estimation of the parameters and prediction of future record values for the power Lindley distribution. First, the maximum likelihood estimate of the parameters and their asymptotic confidence intervals are obtained. Next, we consider Bayes estimation under the symmetric (squared error) and asymmetric (linear-exponential (LINEX)) loss functions by using the joint bivariate density function. Since the closed forms of the estimates are not available, we encounter some computational difficulties to evaluate the Bayes estimates of the parameters involved in the model. For this reason, we use Tierney and Kadane’s method as well as Markov Chain Monte Carlo (MCMC) procedure to compute approximate Bayes estimates. We further consider the non-Bayesian and Bayesian prediction for future lower record arising from the power Lindley distribution based on record data. The comparison of the derived predictors is carried out by using Monte Carlo simulations. A real data set is analyzed for illustration purposes.

A new survival model with surviving fraction: An application to colorectal cancer data.

We propose a new survival model for lifetime data in the presence of surviving fraction and obtain some of its properties. Its genesis is based on extensions of the promotion time cure model, where an extra parameter controls the heterogeneity or dependence of an unobserved number of lifetimes. We construct a regression model to evaluate the effects of covariates in the cured fraction. We discuss inference aspects for the proposed model in a classical approach, where some maximum likelihood tools are explored. Further, an expectation maximization algorithm is developed to calculate the maximum likelihood estimates of the model parameters. We also perform an empirical study of the likelihood ratio test in order to compare the promotion time cure and the proposed models. We illustrate the usefulness of the new model by means of a colorectal cancer data set.

Parametric Analysis of Renal Failure Data using the Exponentiated Odd Weibull Distribution

In this article, we analyze renal failure data from patients with mesangioproliferative glomerulonephritis (MPGN) which was modeled by [1] non-parametrically using the Kaplan-Meier curve. In their work, they showed that the clinical variables, large increase serum creatinine (LISC) and systolic blood pressure >160 mmHg (SBP>160), and morphological variables, benign nephrosclerosis present (BNP) and interstitial score group 5-6 (IS5-6) were part of the variables which indicated progression to end-stage renal failure (ESRF). Though survival curves associated with these variables may be difficult to model by existing parametric distributions in literature. Therefore, we introduce a four-parameter Odd Weibull extension, the exponentiated Odd Weibull (EOW) distribution which is very versatile in modeling lifetime data that its hazard function exhibits ten different hazard shapes as well as various density shapes. Basic properties of the EOW distribution are presented. In the presence of random censoring, a small simulation study is conducted to assess the coverage probabilities of the estimated parameters of the EOW distribution using the maximum likelihood method. Our results show that the EOW distribution is very convenient and reliable to analyze the MPGN data since it provides an excellent fit for the variables LISC, SBP>160, BNP, and IS5-6. Furthermore, advantages of using the EOW distribution over the Kaplan-Meier curve are discussed. Comparisons of the EOW distribution with other Weibull-related distributions are also presented.

Kumaraswamy Exponentiated Chen Distribution for Modelling Lifetime Data

In this paper we introduce the Kumaraswamy exponentiated Chen distribution for modelling a bathtub-shaped hazard rate function. Some structural properties of the Kumaraswamy exponentiated Chen distribution are discussed. The method of maximum likelihood is used for estimating the model parameters. Finally, the flexibility of the proposed distribution is illustrated using reliability data.