arXiv subjects

Sudheesh K. Kattumannil

Publications and source records attributed to Sudheesh K. Kattumannil.

13 recordsLinked to original sources

arXiv2026

Weighted Cumulative Residual Mathai-Haubold Entropy

In this paper, we introduce the weighted cumulative residual Mathai--Haubold entropy and establish its fundamental properties. A dynamic version is developed, and its behavior under linear transformations is studied. Bounds and explicit expressions for some lifetime distributions are derived. Characterization results based on the associated measure are obtained and two new classes of life distributions are formulated. A goodness-of-fit test for the Rayleigh distribution is proposed and its performance is evaluated through a Monte Carlo simulation study. Applications to real data sets demonstrate the practical applicability of the proposed methodology

stat.ME↗

arXiv2026

Empirical Likelihood Inference for Sen and Sen--Shorrocks--Thon Indices

The Sen index and Sen-Shorrocks-Thon (SST) index are widely used measures of poverty indices. Developing reliable inference for these measures enables us to compare these measures in different populations of interest in an effective way. It is important to construct confidence intervals for the Sen index and SST index, which provide better coverage probability and shorter interval length. Motivated by this, we discuss empirical likelihood (EL) and jackknife empirical likelihood (JEL) based inference for the Sen index. To derive a JEL-based confidence interval for the Sen and SST indices, we propose a new estimator for the Sen index using the theory of U-statistics and examine its properties. The large sample properties of the EL and JEL ratio statistics are studied. We also discuss EL and JEL-based inference for the Sen-Shorrocks-Thon (SST) index. The finite sample performance of the EL and JEL-based confidence intervals of both Sen and SST indices is evaluated through a Monte Carlo simulation study. Finally, we illustrate our methods using individual-level data from the Panel Study of Income Dynamics (PSID) survey from the US as well as Indian household level income data for different states sourced from the Consumer Pyramids Household Survey (CPHS).

stat.ME↗

arXiv2026

A unified testing approach for log-symmetry using Fourier methods

Continuous and strictly positive data that exhibit skewness and outliers frequently arise in many applied disciplines. Log-symmetric distributions provide a flexible framework for modeling such data. In this article, we develop new goodness-of-fit tests for log-symmetric distributions based on a recent characterization. These tests utilize the characteristic function as a novel tool and are constructed using an $L^2$-type weighted distance measure. The asymptotic properties of the resulting test statistic are studied. The finite-sample performance of the proposed method is assessed via Monte Carlo simulations and compared with existing procedures. The results under a range of alternative distributions indicate superior empirical power, while the proposed test also exhibits substantial computational efficiency compared to existing methods. The methodology is further illustrated using real data sets to demonstrate practical applicability.

stat.ME↗

arXiv2025

The Cumulative Residual Mathai--Haubold Entropy and its Non-parametric Inference

We introduce the cumulative residual Mathai--Haubold entropy (CRMHE) and investigate its properties. We then propose a dynamic counterpart, the dynamic cumulative residual Mathai--Haubold entropy (DCRMHE), and establish its uniqueness in characterizing the distribution function. Non-parametric estimators for the CRMHE and DCRMHE are developed based on the kernel density estimation of the survival function. The efficacy of the estimators is assessed through a comprehensive Monte Carlo simulation study. The relevance of the proposed DCRMHE estimator is illustrated using two real-world datasets: on the failure times of 70 aircraft windshields and failure times of 40 randomly selected mechanical switches.

stat.ME↗

arXiv2025

JEL ratio test for independence between a continuous and a categorical random variable

The categorical Gini covariance is a dependence measure between a numerical variable and a categorical variable. The Gini covariance measures dependence by quantifying the difference between the conditional and unconditional distributional functions. The categorical Gini covariance equals zero if and only if the numerical variable and the categorical variable are independent. We propose a non-parametric test for testing the independence between a numerical and categorical variable using a modified categorical Gini covariance. We used the theory of U-statistics to find the test statistics and study the properties. The test has an asymptotic normal distribution. Since the implementation of a normal-based test is difficult, we develop a jackknife empirical likelihood (JEL) ratio test for testing independence. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed JEL ratio test. We illustrate the test procedure using Iris flower data set.

stat.ME↗

arXiv2025

Jackknife Empirical Likelihood Ratio Test for Cauchy Distribution

Heavy-tailed distributions, such as the Cauchy distribution, are acknowledged for providing more accurate models for financial returns, as the normal distribution is deemed insufficient for capturing the significant fluctuations observed in real-world assets. Data sets characterized by outlier sensitivity are critically important in diverse areas, including finance, economics, telecommunications, and signal processing. This article addresses a goodness-of-fit test for the Cauchy distribution. The proposed test utilizes empirical likelihood methods, including the jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL). Extensive Monte Carlo simulation studies are conducted to evaluate the finite sample performance of the proposed test. The application of the proposed test is illustrated through the analysing two real data sets.

math.ST↗

arXiv2025

On Weighted Entropy Generating Function

In this paper, we study the properties of the weighted entropy generating function (WEGF). We also introduce the weighted residual entropy generating function (WREGF) and establish some characterization results based on its connections with the hazard rate and the mean residual life function. Furthermore, we propose two new classes of life distributions derived from WREGF. We also study the non-parametric estimation of WREGF. A non-parametric test for the Pareto type I distribution is developed based on entropy characterization. To evaluate the performance of the test statistics, we conduct an extensive Monte Carlo simulation study. Finally, we apply the proposed method to two real-life datasets.

stat.ME↗

arXiv2025

On testing the class of symmetry using entropy characterization and empirical likelihood approach

In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the jackknife empirical likelihood and the adjusted jackknife empirical likelihood ratio tests. The asymptotic properties of the proposed test statistics are studied. We conduct extensive Monte Carlo simulation studies to assess the finite sample performance of the proposed tests. The simulation results indicate that the jackknife empirical likelihood and adjusted jackknife empirical likelihood ratio tests show better performance than the existing tests. Finally, two real data sets are analysed to illustrate the applicability of the proposed tests.

math.ST↗

arXiv2024

Nonparametric goodness of fit tests for Pareto type-I distribution with complete and censored data

Two new goodness of fit tests for the Pareto type-I distribution for complete and right censored data are proposed using fixed point characterization based on Steins type identity. The asymptotic distributions of the test statistics under both the null and alternative hypotheses are obtained. The performance of the proposed tests is evaluated and compared with existing tests through a Monte Carlo simulation experiment. The newly proposed tests exhibit greater power than existing tests for the Pareto type-I distribution. Finally, the methodology is applied to real-world data sets.

stat.ME↗

arXiv2024

Weighted cumulative residual Entropy Generating Function and its properties

The study on the generating function approach to entropy become popular as it generates several well-known entropy measures discussed in the literature. In this work, we define the weighted cumulative residual entropy generating function (WCREGF) and study its properties. We then introduce the dynamic weighted cumulative residual entropy generating function (DWCREGF). It is shown that the DWCREGF determines the distribution uniquely. We study some characterization results using the relationship between the DWCREGF and the hazard rate and/or the mean residual life function. Using a characterization based on DWCREGF, we develop a new goodness fit test for Rayleigh distribution. A Monte Carlo simulation study is conducted to evaluate the proposed test. Finally, the test is illustrated using two real data sets.

math.ST↗

arXiv2024

Jackknife empirical likelihood ratio test for testing the equality of semivariance

Semivariance is a measure of the dispersion of all observations that fall above the mean or target value of a random variable and it plays an important role in life-length, actuarial and income studies. In this paper, we develop a new non-parametric test for equality of upper semi-variance. We use the U-statistic theory to derive the test statistic and then study the asymptotic properties of the test statistic. We also develop a jackknife empirical likelihood (JEL) ratio test for equality of upper Semivariance. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed JEL-based test. We illustrate the test procedure using real data.

stat.ME↗

arXiv2021

A new goodness of fit test for gamma distribution with censored observations

In the present paper, we develop a new goodness fit test for gamma distribution using the fixed point characterization. U-Statistic theory is employed to derive the test statistic. We discuss how the right censored observations are incorporated in the test developed here. The asymptotic properties of the test statistic in both censored and uncensored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We also illustrate the test procedure using several real data sets.

stat.ME↗

arXiv2021

A new goodness of fit test for uniform distribution with censored observations

Using fixed point characterization, we develop a new goodness of fit test for uniform distribution. We also discuss how the right censored observations can be incorporated in the proposed test procedure. We study the asymptotic properties of the proposed test statistics. A Monte Carlo simulation is carried out to evaluate the finite sample performance of the tests. We illustrate the test procedures using real data sets.

stat.ME↗