International Journal of Statistics and Probability, Issue: Vol.15, No.3

Correction to Covariate Selection Strategy for the Extended Propensity Score to Adjust for Missing Not at Random Data

Mon, 05 Oct 2026 07:57:10 +0000

This corrects the article ” Covariate Selection Strategy for the Extended Propensity Score to Adjust for Missing Not at Random Data”, International Journal of Statistics and Probability, 13(4), 26. https://doi.org/10.5539/ijsp.v13n4p26

Bias Reduction for Nonparametric Density Estimator with Standard Kernels

Wed, 30 Sep 2026 00:10:48 +0000

Kernel density estimation (KDE) is a widely used nonparametric tool for recovering unknown probability density functions without strong distributional assumptions. However, even well-tuned kernel density estimators often exhibit non-negligible bias, which can potentially affect the accuracy of subsequent statistical inference. In this paper, we adapt the bias-reduction approach of Cheng et al. (2018), originally proposed for kernel regression, to the classical kernel density estimator. The resulting method reduces the order of magnitude of the asymptotic bias while maintaining the variance at the same order as that of the standard estimator. Unlike traditional bias-reduction strategies based on higher-order kernels or variable kernels, our approach has a simple computational structure and does not require oscillatory kernel functions or pilot estimates for local bandwidths. We derive the theoretical properties of the proposed estimator and assess its performance through simulation studies and two real-data applications. The results show that the bias-reduced estimator often achieves lower mean integrated squared errors than the standard KDE, particularly for finite samples and high-curvature target densities.

A Kinetic-Theory Model of the Neutrino Mass

Wed, 30 Sep 2026 00:14:25 +0000

We present a kinetic-theory estimate of the mass of a particle and apply it to the neutrino. The method rests on two relations of the kinetic theory of gases, recently placed on a rigorous binary-collision footing: a mass—speed relation $m_1u_1^2=m_2u_2^2$, linking two coexisting species through their root-mean-square collision speeds, and a wave--speed relation $u=c\sqrt{3/\gamma}$, converting a medium's propagation speed into its particle collision speed. If neutrinos and ordinary gas molecules are modelled as two species of a common kinetic system obeying Avogadro's law, these relations fix the neutrino mass at $0.025$--$0.042\ \mathrm{eV}/c^2$---at the level of the tightest current neutrino-mass bounds and, as we show, independent of the reference gas. The argument uses the standard control volumes (``boxes'') of the kinetic theory of gases and is a statistical-mechanics estimate: it requires neither the physical confinement of neutrinos nor any direct measurement of neutrino pressure. The estimate is linear in the assumed shared temperature; we set out the governing assumptions explicitly---including the reference temperature and the classical (non-relativistic) kinetic treatment---and identify their relaxation, and the resulting refinements, as directions for future work.

A New Non-Parametric Test for UBAC Lifetime Distributions With Applications to Real Medical Data

Wed, 30 Sep 2026 04:13:27 +0000

This paper introduces a non-parametric test for assessing whether a lifetime distribution belongs to the Used Better than Aged in Convex Ordering (UBAC) class, using Laplace transform ordering. The proposed test addresses a fundamental problem in survival and reliability analysis: distinguishing exponentiality from more general ageing behaviour. Unlike existing approaches, the method accommodates both complete and right-censored data and provides simulated critical values over a wide range of sample sizes.

The asymptotic properties of the test are studied within Pitman’s framework, and its relative efficiency is evaluated against well-known alternatives such as the Weibull, Linear Failure Rate (LFR), and Makeham distributions. Extensive Monte Carlo simulations demonstrate that the proposed procedure maintains good power and stability, even for small samples. The practical relevance of the test is illustrated through applications to several real medical data sets, including leukemia, COVID-19 mortality, liver cancer, and lung cancer survival data. Overall, the proposed method offers a statistically sound and computationally tractable tool for applied researchers in reliability engineering and biomedical survival analysis.

Type-2 Topp-Leone Poisson-G Distribution with Applications of Bur XII Distribution to Censored data

Fri, 09 Oct 2026 15:04:20 +0000

We propose a new method of adding two shape parameters to a family of distributions for more flexibility and wider scope of applications. The method involves the compounding of two family, namely the Poisson family and the Type-2 Topp Leone family resulting in a flexible family called the Type-2 Topp Leone Poisson-g distribution. A special case of the family has been considered called Type-2 Topp Leone Poisson Burr XII distribution. Several properties of the proposed distribution are investigated, including explicit expressions for the moments, quantiles, moment generating function, mean and median deviation, mean residual and mean mean activity time, order statistics and expression of the Renyi and Tsallis entropies are derived. The maximum likelihood estimator technique is used to obtain the values of the unknown parameters. Simulation study is also carried out to determine the effectiveness of the maximum likelihood estimation technique. Two data sets have been analyzed to demonstrate the applicability of the proposed models in practice.