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Asok K. Nanda

Publications and source records attributed to Asok K. Nanda.

18 recordsLinked to original sources
arXiv2026

Estimation of Tsallis entropy and its applications to goodness-of-fit tests

In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis divergence measure. We compare the performance of the proposed estimators by means of bias and mean squared error and also examine their robustness to outliers. Next, we propose a spacings-based estimator for Tsallis entropy under progressive type-II censoring and study its performance using Monte Carlo simulations. Another estimator for Tsallis entropy is proposed using quantile function and its consistency and asymptotic normality are studied, and its performance is evaluated through Monte Carlo simulations. Goodness-of-fit tests for normal and exponential distributions as applications are developed using Tsallis divergence measure. The performance of the proposed tests are then compared with some known tests using simulations and it is shown that the proposed tests perform very well. Also, an exponentiality test under progressive type-II censoring is proposed, its performance is compared with an existing entropy-based test using simulation. It is observed that the proposed test performs well. Finally, some real data sets are analysed for illustrative purposes.

stat.ME↗
arXiv2026

On estimation of weighted cumulative residual Tsallis entropy for complete and censored samples

Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure. Next, we propose some non-parametric estimators of this measure. Asymptotic properties of these estimators are discussed. Performance of these estimators are compared by mean squared error. Non-parametric estimators for weighted cumulative residual entropy measure are also discussed. Estimator for weighted cumulative residual Tsallis entropy for progressive type-II censored data is proposed and its performance is investigated by Monte-Carlo simulations for various censoring schemes. Two uniformity tests for complete samples are proposed based on an estimator of these two measures and power of the tests are compared with some popular tests. The tests perform reasonably well. Uniformity test under progressively type-II censored data is also developed. Some real datasets are analysed for illustration.

math.ST↗
arXiv2021

Departure-based Asymptotic Stochastic Order for Random Processes

We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values coming from two different homogeneous samples, as the sample size becomes large.

math.PR↗
arXiv2021

Conditional Precedence Orders for Stochastic Comparison of Random Variables

Most of the stochastic orders for comparing random variables, considered in the literature, are afflicted with two main drawbacks: (i) lack of connex property and (ii) lack of consideration of any dependence structure between the random variables. Both these drawbacks can be overcome at the cost of transitivity with the stochastic precedence order, which may seem to be a good choice in particular when only two random variables are under consideration, a situation where the question of transitivity does not arise. In this paper, we show that even under such favorable conditions, stochastic precedence order may direct to misleading conclusion in certain situations and develop variations of the order to address the phenomenon.

stat.ME↗
arXiv2021

Asymptotic Stochastic Comparison of Random Processes

Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and interrelations of the orders are discussed. Sufficient conditions for these orders to hold for certain stochastic processes, evolving from some statistical entities of interest, are derived.

math.PR↗
arXiv2020

Reliability study of series and parallel systems of heterogeneous component lifetimes under proportional odds model

In this paper, we investigate various stochastic orderings for series and parallel systems with independent and heterogeneous components having lifetimes following the proportional odds model. We also investigate comparisons between system with heterogeneous components and that with homogeneous components. This paper also studies relative ageing orders for two systems in the framework of components having lifetimes following the proportional odds model.

math.ST↗
arXiv2019

Errors Due to Departure from Independence in Exponential Series System

In reliability and life testing when the exponentially distributed components are put in series, it is generally assumed that the lifetimes of the components are independently distributed, which leads to some errors if they are not actually independent. In this paper, we study the relative errors incurred in different reliability measures due to such assumptions when actually they follow some bivariate exponential distributions.

math.ST↗
arXiv2017

Some Ageing Properties of Dynamic Additive Mean Residual Life Model

Although proportional hazard rate model is a very popular model to analyze failure time data, sometimes it becomes important to study the additive hazard rate model. Again, sometimes the concept of the hazard rate function is abstract, in comparison to the concept of mean residual life function. A new model called `dynamic additive mean residual life model' where the covariates are time-dependent has been defined in the literature. Here we study the closure properties of the model for different positive and negative ageing classes under certain condition(s). Quite a few examples are presented to illustrate different properties of the model.

math.ST↗
arXiv2017

Reliability study of proportional odds family of discrete distributions

The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as Marshall-Olkin family of distributions or Marshall-Olkin extended distributions. In this paper, we consider Marshall-Olkin family of distributions in discrete case with fixed tilt parameter. We study different ageing properties, as well as different stochastic orderings of this family of distributions. All the results of this paper are supported by several examples.

math.ST↗
arXiv2016

Some Reliability Properties of Transformed-Transformer Family of Distributions

The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $ω$ of the cumulative distribution function of $X$. In this paper, we study different stochastic ageing properties, as well as different stochastic orderings of this family of distributions. We discuss the results with several well known distributions.

stat.ME↗
arXiv2016

On Stochastic Comparison Between Two Coherent Systems

Stochastic orders are very useful tool to compare the lifetimes of two coherent systems. We show that, under certain conditions, a coherent system of used components performs better (worse) than a used coherent system with respect to different stochastic orders. Some results on stochastic comparison between a coherent system of inactive components and an inactive coherent system are also discussed.

stat.AP↗
arXiv2016

A Note on Warm Standby System

In this note, we investigate, under what circumstances, a warm standby system (formed by n active components and m warm standby components) has more number of surviving warm standby components than another similar system at the time of $k$th failure of the active component of the respective system. The number of such components being random, the comparison has been done with respect to different stochastic orders, viz. usual stochastic order, hazard rate and reversed hazard rate orders, and likelihood ratio order.

math.PR↗
arXiv2016

Ordering Properties of Order Statistics from Heterogeneous Generalized Exponential and Gamma Populations

Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $θ_i$ and scale parameter $λ_i$ (resp. $δ_i$), $i=1,2,\ldots, n$. Here it is shown that if $\left(λ_1, λ_2,\ldots,λ_n\right)$ is $p$-larger than (resp. weakly supermajorizes) $\left(δ_1,δ_2,\ldots,δ_n\right)$, then $X_{n:n}$ will be greater than $Y_{n:n}$ in usual stochastic order (resp. reversed hazard rate order). That no relation exists between $X_{n:n}$ and $Y_{n:n}$, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if $Y_i$ follows generalized exponential distribution with parameters $\left(\barλ,θ_i\right)$, where $\barλ$ is the mean of all $λ_i$'s, $i=1\ldots n$, then $X_{n:n}$ is greater than $Y_{n:n}$ in likelihood ratio ordering. Some new results on majorization have been developed which fill up some gap in the theory of majorization. Some results on multiple-outlier model are also discussed. In addition to this, we compare two series systems formed by gamma components with respect to different stochastic orders.

stat.AP↗
arXiv2014

On Some Generalized Orderings: In the Spirit of Relative Ageing

We introduce some new generalized stochastic orderings (in the spirit of relative ageing) which compare probability distributions with the exponential distribution. These orderings are useful to understand the phenomenon of positive ageing classes and also helpful to guide the practitioners when there are crossing hazard rates and/or crossing mean residual lives. We study some characterizations of these orderings. Inter-relations among these orderings have also been discussed.

stat.AP↗
arXiv2014

On some generalized ageing orderings

Some partial orderings which compare probability distributions with the expo- nential distribution, are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which de- scribe the same kind of characterization of some generalized ageing classes. We give some equivalent conditions for each of the orderings. Inter-relations among the generalized orderings have also been discussed.

stat.AP↗
arXiv2014

Parameter Estimates of General Failure Rate Model: A Bayesian Approach

The failure rate function plays an important role in studying the lifetime distributions in reliability theory and life testing models. A study of the general failure rate model $r(t)=a+bt^{θ-1}$, under squared error loss function taking $a$ and $b$ independent exponential random variables has been analyzed in the literature. In this article, we consider $a$ and $b$ not necessarily independent. The estimates of the parameters $a$ and $b$ under squared error loss, linex loss and entropy loss functions are obtained here.

stat.CO↗
arXiv2013

General Standby Component Allocation in Series and Parallel Systems

Optimum lifetime of a series (resp. parallel) system with general standby component(s) always depends on allocation strategy of standby component(s) into the system. Here, we discuss three different models of one or more standby compo- nents. In each model, we compare different series (resp. parallel) systems (which are formed through different allocation strategies of standby component(s)) with respect to the usual stochastic and the stochastic precedence orders.

stat.AP↗