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Even though the proportional hazards model has been used extensively in reliability and survival analysis, it often fails to satisfy the basic assumptions wherein additive hazard model is a good alternative. Unlike the distribution function, quantile function are of efficient alternatives in the modelling and analysis of lifetime data. Motivated by these, in the present study we introduce an additive hazards quantile model and study its various properties and applications. The proposed model possess some interesting properties that are not shared by its distribution function counterpart. We also present a class of distributions with quadratic hazard quantile function and examine its usefulness through real-life examples. [ABSTRACT FROM AUTHOR]

In the present work, we propose a method of constructing Archimedean copulas using the total time on test transform, extensively used in reliability modelling. It is observed that the copula can be specified in terms of a univariate life distribution with a finite mean and monotone hazard rate. We discuss some new properties of the Kendall distribution arising from the proposed new generator and the associated measures of dependence. [ABSTRACT FROM AUTHOR]

The role of quantile functions in modeling various forms of statistical data is well established. Generally classical procedures like method of moments, L-moments, percentiles etc are employed in estimating the parameters of the model. In the present work an attempt is made to infer parameters in the Bayesian framework with special emphasis to distributions in which the quantile functions do not posses tractable distribution functions. The procedure is illustrated for some distributions and real life data. [ABSTRACT FROM AUTHOR]

Proportional Hazards Model (PHM) introduced by Cox (1972) is extensively studied in literature. In this paper, we study reliability properties of the PHM using quantile functions. Some special properties of the quantile function, which are not shared by distribution function are explored to study various properties of the PHM. We discuss ageing properties and stochastic orders for the PHM. The quantile-based dynamic cumulative Kullback-Leibler divergence of PHM is studied. Characterizations of some important quantile densities using PHM are also proved. [ABSTRACT FROM AUTHOR]

The paper introduces a quantile-based cumulative Kullback-Leibler divergence and study its various properties. Unlike the distribution function approach, the quantile-based measure possesses some unique properties. The quantile functions used in many applied works do not have any tractable distribution functions where the proposed measure is a useful tool to compute the distance between two random variables. Some useful bounds are obtained for quantile-based residual cumulative Kullback-Leibler divergence and quantile-based reliability measures. Characterization results based on the functional forms of quantile-based residual Kullback-Leibler divergence are obtained for some well-known life distributions, namely exponential, Pareto II and beta. [ABSTRACT FROM AUTHOR]

The existence and the usefulness of discrete bathtub-shaped and upside down bathtub-shaped distributions have been demonstrated in some papers of recent origin. However, the general properties of these two classes of distributions do not seem to have been discussed. This article proposes to study some reliability properties of such distributions. We investigate the closure properties with reference to convolution, mixing, series and parallel systems, etc. and existence of bounds on reliability functions, moment properties, and convergence. [ABSTRACT FROM AUTHOR]

There have been several works aimed at the determination of the shape of the hazard rate when lifetime is treated as continuous. In the present work, we establish some theorems, that enable the identification of the nature of discrete hazard rates. Further, some applications of the results to construct new discrete bathtub-shaped distributions are also proposed. [ABSTRACT FROM AUTHOR]

There has been recent interest in studying the potential of odds function and odds rate in lifetime data analysis. In the present study, we define odds function and odds rate for discrete lifetime distributions. The relationships of these measures with other reliability concepts are discussed. We present the usual aging properties in terms of these measures. The comparison of various reliability concepts of two lifetimes by stochastic orders of their odds functions is investigated. Finally, we apply the proposed results to two real life data. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study a class of distributions that has linear hazard quantile function. Various distributional properties and reliability characteristics of the class are studied. Some characterizations of the class of distributions are presented. The method of L-moments is employed to estimate parameters of the class of distributions. Finally, we apply the proposed class to a real data set. [ABSTRACT FROM PUBLISHER]

Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss distributional and geometric properties of the first and second order partial moments defined in terms of quantile function. Relationships of the scaled stop-loss transform curve with the Lorenz, Gini, Bonferroni and Leinkuhler curves are developed. [ABSTRACT FROM AUTHOR]

We present a new criterion for ageing that characterizes continuous life distributions and a relative ageing factor that measures the effect of ageing of a unit with a specified age in relation to a new unit with the same life distribution. The properties of the criterion are discussed and compared with the other existing concepts of ageing. [ABSTRACT FROM PUBLISHER]

Abstract: The mean, variance and coefficient of variation of residual life which are based on the usual moments of the residual life distribution are extensively used in reliability analysis. It has been established in various theoretical and empirical studies that the L-moments have some advantages over the usual moments in many situations. Accordingly in the present paper we study the properties of L-moments of residual life in the context of modeling lifetime data, characterizing life distributions and other applications. The role of certain quantile functions and quantile-based concepts in reliability analysis are also investigated. [Copyright &y& Elsevier]

In the present paper we derive some identities connecting the failure rate functions and moments of residual life of the nth order equilibrium distribution and the baseline distribution. These identities are used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution by relationships between various reliability characteristics. An approach using the characteristic functions is also discussed with illustrations. [ABSTRACT FROM AUTHOR]

Quantile functions are equivalent alternatives to distribution functions in modeling and analysis of statistical data. The present article discusses the role of quantile functions in reliability studies. We present the hazard, mean residual, variance residual, and percentile residual quantile functions, their mutual relationships and expressions for the quantile functions in terms of these functions. Further, some theoretical results relating to the Hankin and Lee (2006) lambda distribution are discussed. [ABSTRACT FROM AUTHOR]

In this paper we study the properties of total time on test transforms of order n and examine their applications in reliability analysis. It is shown that the successive transforms produce either distributions with increasing or bathtub-shaped failure rates or distributions with decreasing or upside bathtub-shaped failure rates. The ageing properties of the baseline distribution is compared with those of transformed distributions, and a partial order based on nth-order transforms and their implications are discussed. [ABSTRACT FROM AUTHOR]

In the present paper a general theorem that links characterizations of discrete life distributions based on relationship between failure rate and conditional expectations with those in terms of Chernoff-type inequalities is proposed. Exact expression for lower bounds to the variance is calculated for distributions belonging to the modified power series family, Ord family and mixture geometric models. It is shown that the bounds obtained here contain the Cramer–Rao and Chapman–Robbins inequalities as special cases. An application of the results to real data is also provided. [ABSTRACT FROM AUTHOR]

In the present paper the distribution theory of maximum and minimum of the rth concomitants from k independent subgroups each of same size m from the Morgenstern family is investigated. Some applications of the results in estimation of the scale parameter of a marginal variable in the bivariate uniform distribution and a selection problem are discussed. [ABSTRACT FROM AUTHOR]

We generalize some of the existing results on characterization of continuous distributions by lower bound on the variance and point out their equivalence to characterization of life distributions by relationship between conditional expectation and failure (reversed failure) rate. It is shown that these lower bounds are the same as, Cramer–Rao bound in the regular case and improves upon the latter in the non-regular case. Some applications to reliability modeling and catastrophe theory are pointed out. [ABSTRACT FROM AUTHOR]

In this article, we investigate models that exhibit constant total failure rate (Sun, K., Basu, A. P. (1995). A characterization of a bivariate geometric distribution. Statistics and Probability Letters 23:307-311) and study the property in relation to the bivariate lack of memory property (BLMP). [ABSTRACT FROM AUTHOR]

In this paper the class of continuous bivariate distributions that has form-invariant weighted distribution with weight function $w\lpar x_{1}\comma \; x_{2}\rpar = x_{1}^{\alpha_{1}} x_{2}^{\alpha_{2}}$ is identified. It is shown that the class includes some well known bivariate models. Bayesian inference on the parameters of the class is considered and it is shown that there exist natural conjugate priors for the parameters. [ABSTRACT FROM AUTHOR]

Presents information on a study which analyzed an extended class of Pearson system of distributions in the context of reliability. Extended class and a characterization theorem; Method used to identify an increasing (decreasing) failure rate model in the generalized Pearson system; Lemma; Theorem.

Characterizes the Pearson family of distributions by finding a relationship between the failure rate and the higher order moments of residual life.

Abstract: This paper starts by introducing extreme wave height analysis using quantile functions, which are an alternative to the classical approaches to model long term maxima or extreme values. The long-term distribution of significant wave heights from four locations are modelled with Davies, 3-parameter Weibull, generalized extreme value (GEV) and generalized Pareto (GP3) quantile functions. Even though the 3-parameter Weibull and GP3 quantile functions are adequate wave height models in this study, the performance of the Davies quantile function for extreme wave analysis seems to be consistently good both temporally and spatially. [Copyright &y& Elsevier]

Abstract: Calibration coefficients incorporated in the modified Weibull distribution are more effective for maximum wave height simulation. The parametric relations are derived there from to estimate various wave height statistics including extreme wave heights. The characteristic function of the Weibull distribution is derived. The Weibull distribution is suggested for the newly defined significant wave height simulation by the method of characteristic function. The statistical tools suggested and developed here for predicting the required wave height statistics are validated against the wave data (both deep and shallow) of eastern Arabian Sea comprising rough monsoon conditions also, giving reasonable accuracy. [Copyright &y& Elsevier]