A Software Reliability Model Using Quantile Function

We study a class of software reliability models using quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. Inference procedures on parameters of the model based on L-moments are studied. We apply the proposed model to a real data set

Quantile Based Relevation Transform and its Properties

Relevation transform introduced by Krakowski (1973) is extensively studied in the literature. In this paper, we present a quantile based definition of the relevation transform and study its properties in the context of lifetime data analysis. We give important special cases of relevation transform in the context of proportional hazards and equilibrium models in terms of quantile function

Modeling lifetime data with multiple causes using cause specific reversed hazard rates

In this paper we introduce and study cause specific reversed hazard rates in the context of left censored lifetime data with multiple causes. Nonparametric inference procedure for left censored lifetime data with multiple causes using cause specific reversed hazard rate is discussed. Asymptotic properties of the estimators are studied. Simulation studies are conducted to assess the efficiency of the estimators. Further, the proposed method is applied to mice mortality data (Hoel 1972) and Australian twin data (Duffy et al. 1990)

Regression Analysis of Cure Model with Generalised Weibull Distribution

Cure models are of special attention when all of the study subjects do not experience the event of interest even after long follow-up time. Many researchers have used exponential, gamma and Weibull distribution in the latency part of parametric cure models. In this article, we propose a new regression model with cured fraction, in its latency part is explained by the generalised Weibull distribution (Mudholkar et al., 1996). The estimation of the parameters of the proposed model is done using maximum likelihood method via EM algorithm. Simulations are carried out to study the effect of sampling fluctuations and to knowthe efficiency of estimators. The proposed model is applied to real data on acute myelogenous leukaemia. The statistical significance of the regression parameter is checked by likelihood ratio (LR) test and the new model was compared withWeibull cure model using Akaike information criterion (AIC)

Some Reliability Properties of Extropy and its Related Measures Using Quantile Function

Extropy is a recent addition to the family of information measures as a complementary dual of Shannon entropy, to measure the uncertainty contained in a probability distribution of a random variable. A probability distribution can be specified either in terms of the distribution function or by the quantile function. In many applied works, there do not have any tractable distribution function but the quantile function exists, where a study on the quantile-based extropy are of importance. The present paper thus focuses on deriving some properties of extropy and its related measures using quantile function. Some ordering relations of quantile-based residual extropy are presented. We also introduce the quantile-based extropy of order statistics and cumulative extropy and studied its properties. Some applications of empirical estimation of quantile-based extropy using simulation and real data analysis are investigated

Characterizations of a family of bivariate Pareto distributions

In the present paper, we study properties of a family of bivariate Pareto distributions. The well known dullness property of the univariate Pareto model is extended to the bivariate setup. Two measures of income inequality viz. income gap ratio and mean left proportional residual income are defined in the bivariate case. We also introduce bivariate generalized failure rate useful in reliability analysis. Characterizations, using the above concepts, for various members of the family of bivariate Pareto distributions are derived

Dynamic Information Volatility Function

Liu (2007) discussed a new measure, known as the information volatility function to study the variability of the uncertainty contained in a probability distribution. In the present paper, we extend this concept to the residual random variable, a dynamic information volatility function and study its usefulness in reliability modelling. Different ageing and characterization properties of dynamic information volatility function are also derived

On the covariance of residual lives

Various properties of residual life such as mean, median, percentiles, variance etc have been discussed in literature on reliability and survival analysis. However a detailed study on covariance between residual lives in a two component system does not seem to have been undertaken. The present paper discusses various properties of product moment and covariance of residual lives. Relationships the product moment has with mean residual life and failure rate are studied and some characterizations are established

A semi-parametric regression model for analysis of middle censored lifetime data

Middle censoring introduced by Jammalamadaka and Mangalam (2003), refers to data arising in situations where the exact lifetime becomes unobservable if it falls within a random censoring interval, otherwise it is observable. In the present paper we propose a semi-parametric regression model for such lifetime data, arising from an unknown population and subject to middle censoring. We provide an algorithm to find the nonparametric maximum likelihood estimator (NPMLE) for regression parameters and the survival function. The consistency of the estimators are established. We report simulation studies to assess the finite sample properties of the estimators. We then analyze a real life data on survival times for diabetic patients studied by Lee et al. (1988)