Search Results (5)

Financial return distributions often exhibit central asymmetry and heavy-tailed extremes, challenging standard parametric models. We propose a novel composite distribution integrating a skew-normal center with skew-t tails, partitioning the support into three regions with smooth junctions. The skew-normal component captures moderate central asymmetry, while the skew-t tails model extreme events with power-law decay, with tail weights determined by continuity constraints and thresholds selected via Hill plots. Monte Carlo simulations show that the composite model achieves superior global fit, lower-tail KS statistics, and stable parameter estimation compared with skew-normal and skew-t benchmarks. We further conduct simulation-based and empirical backtesting of risk measures, including Value-at-Risk (VaR) and Expected Shortfall (ES), using generated datasets and 2083 TSLA daily log returns (2017–2025), demonstrating accurate tail risk capture and reliable risk forecasts. Empirical fitting also yields improved log-likelihood and diagnostic measures (P–P, Q–Q, and negative log P–P plots). Overall, the proposed composite distribution provides a flexible theoretically grounded framework for modeling asymmetric and heavy-tailed financial returns, with practical advantages in risk assessment, extreme event analysis, and financial risk management. Full article

This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and incomplete moments, entropy, and the moment generating function, are derived and examined in a formal manner. Maximum likelihood estimation (MLE) techniques are used for estimation of parameters, as well as a Monte Carlo simulation study to account for estimator performance across varying sample sizes and parameter values. The EPS model is also generalized to a regression paradigm to include covariate data, whose estimation is also conducted via MLE. Practical utility and flexibility of the EPS distribution are demonstrated through two real examples: one for the duration of repairs and another for HIV/AIDS mortality in Germany. Comparisons with some of the existing distributions, i.e., power Zeghdoudi, power Ishita, power Prakaamy, and logistic-Weibull, are made through some of the goodness-of-fit statistics such as log-likelihood, AIC, BIC, and the Kolmogorov–Smirnov statistic. Graphical plots, including PP plots, QQ plots, TTT plots, and empirical CDFs, further confirm the high modeling capacity of the EPS distribution. Results confirm the high goodness-of-fit and flexibility of the EPS model, making it a very good tool for reliability and biomedical modeling. Full article

This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing for greater adaptability to various data shapes. The paper explores several theoretical aspects of the proposed model, including its moments, quantile function and hazard rate. To assess the effectiveness of parameter estimation, a detailed simulation study is conducted using seven estimation techniques: Maximum likelihood estimation (MLE), Cramér–von Mises estimation (CVME), maximum product of spacings estimation (MPSE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson–Darling estimation (ADE) and a right-tailed version of Anderson–Darling estimation (RTADE). The results offer comparative insights into the performance of each method across different sample sizes. The practical value of the NAP-HL distribution is demonstrated using two real datasets from the metrology and engineering domains. In both cases, the proposed model provides a better fit than the traditional half-logistic and related distributions, as shown by lower values of standard model selection criteria. Graphical tools such as fitted density curves, Q–Q and P–P plots, survival functions and box plots further support the suitability of the model for real-world data analysis. Full article

Nonparametric two-sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being designed and analyzed, both for the unidimensional and the multivariate setting. In this short survey, we focus on test statistics that involve the Wasserstein distance. Using an entropic smoothing of the Wasserstein distance, we connect these to very different tests including multivariate methods involving energy statistics and kernel based maximum mean discrepancy and univariate methods like the Kolmogorov–Smirnov test, probability or quantile (PP/QQ) plots and receiver operating characteristic or ordinal dominance (ROC/ODC) curves. Some observations are implicit in the literature, while others seem to have not been noticed thus far. Given nonparametric two-sample testing’s classical and continued importance, we aim to provide useful connections for theorists and practitioners familiar with one subset of methods but not others. Full article

Several graphical methods for testing univariate composite normality from an i.i.d. sample are presented. They are endowed with correct simultaneous error bounds and yield size-correct tests. As all are based on the empirical CDF, they are also consistent for all alternatives. For one test, called the modified stabilized probability test, or MSP, a highly simplified computational method is derived, which delivers the test statistic and also a highly accurate p-value approximation, essentially instantaneously. The MSP test is demonstrated to have higher power against asymmetric alternatives than the well-known and powerful Jarque-Bera test. A further size-correct test, based on combining two test statistics, is shown to have yet higher power. The methodology employed is fully general and can be applied to any i.i.d. univariate continuous distribution setting. Full article