arXiv subjects

Lakshmi Kanta Patra

Publications and source records attributed to Lakshmi Kanta Patra.

11 recordsLinked to original sources

arXiv2026

Parametric bootstrap simultaneous confidence interval based on doubly type-II censoring

Parametric bootstrap and fiducial generalized methods are proposed to construct simultaneous confidence intervals (SCIs) for all pairwise mean differences of several two-parameter exponential distributions, based on doubly censored samples. Both methods have been shown to have correct asymptotic coverage probabilities. Simulation studies are conducted to compare the performance of the two proposed methods. The usefulness of our proposed procedure is illustrated with two examples.

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arXiv2026

Estimating order scale parameters of two scale mixture of exponential distributions

The scale mixture of the exponential distribution provides a flexible framework for modelling lifetime and reliability data. This model is widely used in survival analysis, biomedical studies, statistical finance, and other related disciplines. In this work, we investigate the estimation of the ordered scale parameter of two scale mixture of exponential distributions under Stein loss and symmetric loss functions. Under certain conditions, we prove the inadmissibility of the affine equivariant estimator and exhibit several improved estimators. Consequently, we propose a class of estimators that uniformly dominate the best affine equivariant estimators (BAEE). Furthermore, we have proved that the boundary estimator of this class is a generalized Bayes estimator. As an application, we have proposed improved estimators for the ordered scale parameters of the multivariate Lomax and exponential inverse Gaussian distributions. For each case, we have conducted a simulation study to compare the risk performance of the improved estimators. Finally, we have given two real-life data analysis for implementation purposes.

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arXiv2026

Estimation of differential entropy for normal populations under prior information

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order restrictions. This information should be taken into account to obtain improved estimators. In this paper, we study the problems of point-wise and interval estimation of the entropy of two normal populations under a general location-invariant loss function. For the point-wise estimation, we have derived the maximum likelihood estimator (MLE), restricted MLE and the uniformly minimum variance unbiased estimator (UMVUE). Further, we derive a sufficient condition for improvement over affine equivariant estimators. A class of improved estimators is derived that dominates the best affine equivariant estimator (BAEE). Furthermore, we obtain a class of smooth improved estimator that dominates BAEE. We present special loss functions and derive expressions for the proposed improved estimators. A numerical study is conducted to compare the risk performance of the proposed estimators under quadratic and linex loss functions. For interval estimation, we have derived asymptotic confidence interval, bootstrap confidence intervals, HPD credible interval, and intervals based on generalized pivot variables. A comprehensive numerical comparison of these intervals is carried out in terms of coverage probabilities and average lengths. Finally, the proposed results are illustrated with a real example: the failure of the air-conditioning systems on Boeing 720 jet planes.

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arXiv2026

Estimating ordered variance of two scale mixture of normal distributions

This study investigates component wise estimation of ordered variances of scale mixture of two normal distributions. For this study two special loss functions are considered namely squared error loss function and entropy loss function. We have derived the general improvement results and based on these results the estimators that outperform BAEE are obtained. Moreover under certain sufficient conditions a class of improved estimators is proposed for both loss functions. As a special case of scale mixture of normal distribution the results are applied to the multivariate t-distribution and obtained the improvement results. For this case a detailed numerical comparison is carried out which validates our theoretical findings.

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arXiv2025

Estimating location parameters of several exponential distributions with ordered restriction under Linex loss function

Some improved estimators of the location parameters of several exponential distributions with ordered restriction are derived and compared numerically using Monte Carlo simulations. Note that the two-parameter exponential distribution is very useful in different areas like survival analysis, reliability engineering and biomedical research, where products have a guaranteed failure-free operating time before failures begin to occur. In the present manuscript, we address the component-wise estimation of location parameters of $k~(\ge 2)$ exponential distributions under an asymmetric Linex loss function. The location parameter represents a minimum guaranteed period before failure. At first, we consider the estimation of the location parameters with ordered scale parameters. Next, we address the estimation of ordered location parameters. For this, we take three different cases into account as follows: $(i)$ scale parameters are known, $(ii)$ scale parameters are unknown but equal, $(iii)$ scale parameters are unknown and unequal. In these cases, we establish general inadmissibility results. Further, using the general result, the inadmissibility of the best affine equivariant estimator is proved. The improved estimators are written in explicit forms. Additionally, we show that the results for several important life-testing schemes namely $(i)$ Type-II censoring, $(ii)$ progressive type-II censoring and $(iii)$ record value data can be obtained using i.i.d sample.Finally, for each case, the Monte Carlo simulation technique is used to compare the performance of the proposed estimators based on their risk values. The numerical results reveal a significant improvement of the proposed estimators.

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arXiv2025

Improved estimation of the positive powers ordered restricted standard deviation of two normal populations

The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under a general scale invariant bowl-shaped loss function. Also, we proposed a class of improved estimators. It has been shown that the boundary estimator of this class is a generalized Bayes. As an application, the improved estimators are obtained with respect to quadratic loss, entropy loss, and a symmetric loss function. We have conducted extensive Monte Carlo simulations to study and compare the risk performance of the proposed estimators. Finally, a real life data analysis is given to illustrate our findings.

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arXiv2024

On the improved estimation of ordered parameters based on doubly type-II censored sample

A doubly type-II censored scheme is an important sampling scheme in the life testing experiment and reliability engineering. In the present commutation, we have considered estimating ordered scale parameters of two exponential distributions based on doubly type-II censored samples with respect to a general scale invariant loss function. We have obtained several estimators that improve upon the BAEE. We also propose a class of improved estimators. It is shown that the boundary estimator of this class is generalized Bayes. As an application, we have derived improved estimators with respect to three special loss functions, namely quadratic loss, entropy loss, and symmetric loss function. We have applied these results to special life-testing sampling schemes. Finally, we conducted a simulation study to compare the performance of the improved estimators. A real-life data analysis has been considered for implementation purposes.

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arXiv2024

Estimating location parameters of two exponential distributions with ordered scale parameters

In the usual statistical inference problem, we estimate an unknown parameter of a statistical model using the information in the random sample. A priori information about the parameter is also known in several real-life situations. One such information is order restriction between the parameters. This prior formation improves the estimation quality. In this paper, we deal with the component-wise estimation of location parameters of two exponential distributions studied with ordered scale parameters under a bowl-shaped affine invariant loss function and generalized Pitman closeness criterion. We have shown that several benchmark estimators, such as maximum likelihood estimators (MLE), uniformly minimum variance unbiased estimators (UMVUE), and best affine equivariant estimators (BAEE), are inadmissible. We have given sufficient conditions under which the dominating estimators are derived. Under the generalized Pitman closeness criterion, a Stein-type improved estimator is proposed. As an application, we have considered special sampling schemes such as type-II censoring, progressive type-II censoring, and record values. Finally, we perform a simulation study to compare the risk performance of the improved estimators

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arXiv2023

On improved estimation of the larger location parameter

This paper investigates the problem of estimating the larger location parameter of two general location families from a decision-theoretic perspective. In this estimation problem, we use the criteria of minimizing the risk function and the Pitman closeness under a general bowl-shaped loss function. Inadmissibility of a general location and equivariant estimators is provided. We prove that a natural estimator (analogue of the BLEE of unordered location parameters) is inadmissible, under certain conditions on underlying densities, and propose a dominating estimator. We also derive a class of improved estimators using the Kubokawa's IERD approach and observe that the boundary estimator of this class is the Brewster-Zidek type estimator. Additionally, under the generalized Pitman criterion, we show that the natural estimator is inadmissible and obtain improved estimators. The results are implemented for different loss functions, and explicit expressions for the dominating estimators are provided. We explore the applications of these results to for exponential and normal distribution under specified loss functions. A simulation is also conducted to compare the risk performance of the proposed estimators. Finally, we present a real-life data analysis to illustrate the practical applications of the paper's findings.

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arXiv2023

Inadmissibility of invariant estimator of function of scale parameter of several exponential distributions

In various applied areas such as reliability engineering, molecular biology, finance, etc., the measure of uncertainty of a probability distribution plays an important role. In the present work, we consider the estimation of a function of the scale parameter, namely entropy of many exponential distributions having unknown and unequal location parameters with a common scale parameter. For this estimation problem, we have considered bowl-shaped location invariant loss functions. The inadmissibility of the minimum risk invariant estimator (MRIE) is proved by proposing a non-smooth improved estimator. Also, we have obtained a smooth estimator which improves upon the MRIE. As an application, we have obtained explicit expressions of improved estimators for two well-known loss functions namely squared error loss and linex loss. Further, we have shown that these estimators can be derived for other important censored sampling schemes. At first, we obtained the results for the complete and i.i.d. sample. We have seen that the results can be applied for (i) record values, (ii) type-II censoring, and (iii) progressive Type-II censoring. Finally, a simulation study has been carried out to compare the risk performance of the proposed improved estimators.

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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.

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