arXiv subjects

Suchandan Kayal

Publications and source records attributed to Suchandan Kayal.

32 records · Page 2Linked to original sources

arXiv2023

Extended fractional cumulative past and paired phi-entropy measures

Very recently, extended fractional cumulative residual entropy (EFCRE) has been proposed by Foroghi et al. (2022). In this paper, we introduce extended fractional cumulative past entropy (EFCPE), which is a dual of the EFCRE. The newly proposed measure depends on the logarithm of fractional order and the cumulative distribution function (CDF). Various properties of the EFCPE have been explored. This measure has been extended to the bivariate setup. Furthermore, the conditional EFCPE is studied and some of its properties are provided. The EFCPE for inactivity time has been proposed. In addition, the extended fractional cumulative paired phi-entropy has been introduced and studied. The proposed EFCPE has been estimated using empirical CDF. Furthermore, the EFCPE is studied for coherent systems. A validation of the proposed measure is provided using logistic map. Finally, an application is reported.

math.ST↗

arXiv2023

Estimation of parameters of the logistic exponential distribution under progressive type-I hybrid censored sample

The paper addresses the problem of estimation of the model parameters of the logistic exponential distribution based on progressive type-I hybrid censored sample. The maximum likelihood estimates are obtained and computed numerically using Newton-Raphson method. Further, the Bayes estimates are derived under squared error, LINEX and generalized entropy loss functions. Two types (independent and bivariate) of prior distributions are considered for the purpose of Bayesian estimation. It is seen that the Bayes estimates are not of explicit forms.Thus, Lindley's approximation technique is employed to get approximate Bayes estimates. Interval estimates of the parameters based on normal approximate of the maximum likelihood estimates and normal approximation of the log-transformed maximum likelihood estimates are constructed. The highest posterior density credible intervals are obtained by using the importance sampling method. Furthermore, numerical computations are reported to review some of the results obtained in the paper. A real life dataset is considered for the purpose of illustrations.

stat.AP↗

arXiv2023

Estimating the scale parameters of several exponential distributions under order restriction

In the present work, we have investigated the problem of estimating parameters of several exponential distributions with ordered scale parameters under the linex loss function. We have considered estimating ordered scale parameters when the location parameters are known and unknown. For every case, we consider a class of equivariant estimators, and sufficient condition is obtained under which this class of estimators improves upon the usual estimator. Using this result, we have shown that the restricted maximum likelihood estimator is inadmissible. Finally, for every case, we conduct a simulation study to compare the risk performance of the proposed estimators.

math.ST↗

arXiv2022

Reliability analysis of K-out-of-N system for Weibull components based on generalized progressive hybrid censored data

In this paper, we have investigated the reliability of a K-out-of-N system for the components following Weibull distribution based on the generalized progressive hybrid censored data. We have obtained the maximum likelihood estimates (MLEs) of the unknown parameters and the reliability function of the system. Using asymptotic normality property of MLEs, the corresponding asymptotic confidence intervals are constructed. Furthermore, Bayes estimates are derived under squared error loss function with informative prior by using Markov Chain Monte Carlo (MCMC) technique. Highest posterior density (HPD) credible intervals are obtained. A Monte Carlo simulation study is carried out to compare performance of the established estimates. Finally, a real data set is considered for illustrative purposes.

stat.ME↗

arXiv2022

Weighted fractional generalized cumulative past entropy and its properties

In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied. Bounds and stochastic orderings are derived. A connection between the proposed measure and the left-sided Riemann-Liouville fractional integral is established. Further, the proposed measure is studied for the proportional reversed hazard rate models. Next, a nonparametric estimator of the weighted fractional generalized cumulative past entropy is suggested based on empirical distribution function. Various examples with a real life data set are considered for the illustration purposes. Finally, large sample properties of the proposed empirical estimator are studied.

math.ST↗

arXiv2021

Inadmissibility Results for the Selected Hazard Rates

Let us consider $k ~(\ge 2)$ independent populations $Π_1, \ldots,Π_k$, where $Π_i$ follows exponential distribution with hazard rate ${σ_i},$ ($i = 1,\ldots,k$). Suppose $Y_{i1},\ldots, Y_{in}$ be a random sample of size $n$ drawn from the $i$th population $Π_i$, where $i = 1,\ldots,k.$ For $i = 1,\ldots,k$, consider $Y_i=\sum_{j=1}^nY_{ij}$. The natural selection rule is to select a population associated with the largest sample mean. That is, $Π_i$, ($i = 1,\ldots,k$) is selected if $Y_i=\max(Y_1,\ldots,Y_k)$. Based on this selection rule, a population is chosen. Then, we consider the estimation of the hazard rate of the selected population with respect to the entropy loss function. Some natural estimators are proposed. The minimaxity of a natural estimator is established. Improved estimators improving upon the natural estimators are derived. Finally, numerical study is carried out in order to compare the proposed estimators in terms of the risk values.

math.ST↗

arXiv2021

Fractional generalized cumulative entropy and its dynamic version

Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fractional cumulative entropy as a non-parametric estimator of the new measure. It is shown that the empirical measure converges to the proposed notion almost surely. Then, we address the stability of the empirical measure and provide an example of application to real data. Finally, a central limit theorem is established under the exponential distribution.

math.PR↗

arXiv2021

Failure extropy, dynamic failure extropy and their weighted versions

Extropy was introduced as a dual complement of the Shannon entropy. In this investigation, we consider failure extropy and its dynamic version. Various basic properties of these measures are presented. It is shown that the dynamic failure extropy characterizes the distribution function uniquely. We also consider weighted versions of these measures. Several virtues of the weighted measures are explored. Finally, nonparametric estimators are introduced based on the empirical distribution function.

math.ST↗

arXiv2021

On comparison of the second-order statistics from independent and interdependent exponentiated location-scale distributed random variables

Consider two batches of independent or interdependent exponentiated location-scale distributed heterogeneous random variables. This article investigates ordering results for the second-order statistics from these batches when a vector of parameters is switched to another vector of parameters in the specified model. Sufficient conditions for the usual stochastic order and the hazard rate order are derived. Some applications of the established results are presented.

math.ST↗

arXiv2021

Ordering results between the largest claims arising from two general heterogeneous portfolios

This work is entirely devoted to compare the largest claims from two heterogeneous portfolios. It is assumed that the claim amounts in an insurance portfolio are nonnegative absolutely continuous random variables and belong to a general family of distributions. The largest claims have been compared based on various stochastic orderings. The established sufficient conditions are associated with the matrices and vectors of model parameters. Applications of the results are provided for the purpose of illustration.

q-fin.RM↗

arXiv2021

Some new ordering results on stochastic comparisons of second largest order statistics from independent and interdependent heterogeneous distributions

The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are assumed to follow heterogeneous general exponentiated location-scale models. In this communication, the usual stochastic and reversed hazard rate orders between the systems' lifetimes are established under two cases. For the case of independent random lifetimes, the usual stochastic order and the reversed hazard rate order between the second-largest order statistics are obtained by using the concept of vector majorization and related orders. For the dependent case, the conditions under which the usual stochastic order between the second-largest order statistics holds are investigated. To illustrate the theoretical findings, some special cases of the exponentiated location-scale model are considered.

math.ST↗

arXiv2021

Estimation of parameters of the Gumbel type-II distribution under AT-II PHCS with an application of Covid-19 data

In this paper, we investigate the classical and Bayesian estimation of unknown parameters of the Gumbel type-II distribution based on adaptive type-II progressive hybrid censored sample (AT-II PHCS). The maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) are developed and computed numerically using Newton-Raphson method. Bayesian approaches are employed to estimate parameters under symmetric and asymmetric loss functions. Bayesian estimates are not in explicit forms. Thus, Bayesian estimates are obtained by using Markov chain Monte Carlo (MCMC) method along with the Metropolis-Hastings (MH) algorithm. Based on the normality property of MLEs the asymptotic confidence intervals are constructed. Also, bootstrap intervals and highest posterior density (HPD) credible intervals are constructed. Further a Monte Carlo simulation study is carried out. Finally, the data set based on the death rate due to Covid-19 in India is analyzed for illustration of the purpose.

stat.ME↗

arXiv2020

Ordering results of extreme order statistics from multiple-outlier scale models with dependence

In this paper, we focus on stochastic comparisons of extreme order statistics stemming from multiple-outlier scale models with dependence. Archimedean copula is used to model dependence structure among nonnegative random variables. Sufficient conditions are obtained for comparison of the largest order statistics in the sense of the usual stochastic, reversed hazard rate, star and Lorenz orders. The smallest order statistics are also compared with respect to the usual stochastic, hazard rate, star and Lorenz orders. To illustrate the theoretical establishments, some examples are provided.

math.ST↗

arXiv2020

A probabilistic proof of the finite geometric series

In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.

math.PR↗