Journal of Statistical Sciences

A Nonparametric Test for Stochastic Ordering in Type I Censored ‎Data‎

Ebrahim Amini-Seresht

In this paper, a nonparametric test based on incomplete data is proposed to investigate the usual stochastic order using an extension of Banerjee statistic for Type I censored data. This extension is optimized with weight coefficients based on Simpson's rule and the bootstrap method with 10000 iterations to estimate the empirical distribution of the proposed test statistic. The empirical distribution of the statistic under censoring is studied, and the power of the test is evaluated using Monte Carlo simulations against the Lehmann alternative model.

A Change-point Detection Test in a Class of INAR(1) Processes Using the Empirical Likelihood Method

Sarah Jomhoori

Integer-valued time series models play an essential role in the analysis of dependent count data. One of the main challenges in these models is to detect structural changes over time. These changes may be caused by sudden interventions such as policy changes, pandemics, or system failures. In this paper, the empirical likelihood method is used to detect structural changes in a class of INAR(1) processes. This method is a tool for early warning of structural changes in these processes. Using simulation, the empirical sizes and powers of the test are calculated for different sample sizes, and the test's performance is investigated. Finally, the practical efficiency of the test is investigated by identifying the change point in two real datasets: the number of robberies and the number of COVID-19 deaths.

Forecasting Density Function Time Series: A Functional Singular Spectrum Analysis Approach

Hossein Haghbin

In this paper, a novel approach for forecasting a time sequence of probability density functions is introduced, which is based on Functional Singular Spectrum Analysis (FSSA). This approach is designed to analyze functional time series and address the constraints in predicting density functions, such as non-negativity and unit integral properties. First, appropriate transformations are introduced to convert the time series of density functions into a functional time series. Then, FSSA is applied to forecast the new functional time series, and finally, the predicted functions are transformed back into the space of density functions using the inverse transformation. The proposed method is evaluated using real-world data, including the density of satellite imagery.

Heavy-Tailed Extended Exponential Log-Logistic Distribution: Properties and Applications

Fatemeh Yousefzadeh

Researchers develop generalized families of distributions to better model data in fields like risk management, economics, and insurance. In this paper, a new distribution, the Extended Exponential Log-Logistic Distribution, is introduced, which belongs to the class of heavy-tailed distributions. Some statistical properties of the model, including moments, moment-generating function, entropy, and economic inequality curves, are derived. Six estimation methods are proposed for estimating the model parameters, and the performance of these methods is evaluated using randomly generated datasets. Additionally, several insurance-related measures, including Value at Risk, Tail Value at Risk, Tail Variance, and Tail Variance Premium, are calculated. Finally, two real insurance datasets are employed, showing that the proposed model fits the data better than many existing related models.

Generalization of Discrete Chi-Squared Information Measure and and Its Application in Image Processing

Omid Kharazmi

In this paper, by considering the generalized chi-squared information and the relative generalized chi-squared information measures, discrete versions of these information measures are introduced. Then, generalizations of these information quantities based on their convexity property are presented. Some essential features of these new measures and their relationships are studied. Moreover, the performance of these new information measures is investigated for some well-known and widely used models in coding theory and thermodynamics, such as escort distributions and generalized escort distributions. Finally, two applications of the introduced discrete generalized chi-squared information measure are examined in the context of image quality assessment. In addition, the results obtained from the performance of these measures are compared with the performance of the critical metric, peak signal-to-noise ratio. It is shown that the generalized chi-squared divergence measure exhibits performance similar to the peak signal-to-noise ratio and can be used as an alternative metric.

Development of a Bayesian Model For Finite Mixture Regression of the Skew-Laplace Distribution

Nahid Sanjari Farsipour

In many applications, observations have a skewness, an elongated shape, a heavy tail, a multi-mode structure, or a mixed distribution. Therefore, models based on the normal distribution cannot provide correct inferences under such conditions and can lead to biased estimators or increased variance. The Laplace distribution and its generalizations can be suitable alternatives in such situations due to their elongation, heavy tails, and skewness. On the other hand, in models based on mixed distributions, there is always a possibility that fewer samples are available from one or more components. Therefore, given the Bayesian approach's advantage in handling small samples, this research developed a Bayesian model to fit a finite mixed regression model with skew-Laplace distributions and conducted a simulation study to assess its performance. Laplace has been compared in two approaches, frequentist and Bayesian. The results show that the Bayesian approach of the model is more effective than other models.

Estimation of Conditional Expected Shortfall Based on Copula Function and ARMA-GARCH Time Series Models with Generalized Error Distribution

Mohammad Amini

Events in one financial institution can affect other institutions. For this reason, systemic risk is of interest to risk analysts, and the most important methods of measuring it are the CoVaR and CoES. If there is a dependence between the returns of two financial institutions, Copula functions can be used to examine the structure of the dependence between them. Since return data are often are unstable over time, ARMA-GARCH time series models can be used to model variability. In this paper, CoVaR is evaluated for four copula functions, and then CoES are estimated based on that in ARMA-GARCH models with GED distributions. Then, these two measures are calculated with the returns of Tejarat and Mellat banks.

A New Method for Proving the Preservation of IFR Property in Discrete Order Statistics

Mahdi Alimohammadi

It was proved about 60 years ago that if a continuous random variable X has an increasing failure rate then its order statistics will also be increasing failure rate, and this problem remained unproved for the discrete case until recently a proof method using an integral inequality was provided. In this article, we present a completely different method to solve this problem.

Application of Fuzzy Statistics in Experimental Design Models

Reza Ghasemi

In statistical research, experimental designs are used to investigate the effect of control variables on output responses. These methods are based on the assumption of normal distribution of data and face fundamental challenges in dealing with outliers. The present study examines five different examples of experimental design methods to deal with this challenge: Huber, quadratic, substitution, ranking, and fuzzy regression robustness methods. By providing empirical evidence from real data on seedling growth and weld quality, it is shown that fuzzy can be used as an efficient alternative to conventional methods in the presence of outliers. It is shown that fuzzy not only outperforms the classical experimental design method in the presence of outliers, but also outperforms standard robustness methods in handling outliers.

Using Shape Descriptors in Shape Data Classification

Meisam Moghimbeygi

The classification of shape data is a significant challenge in the statistical analysis of shapes and machine learning. In this paper, we introduce a multinomial logistic regression model based on shape descriptors for classifying labeled configurations. In this model, the explanatory variables include a set of geometric descriptors such as area, elongation, convexity, and circularity, while the response variable represents the category of each configuration. The inclusion of these descriptors preserves essential geometric information and enhances classification accuracy. We evaluate the proposed model using both simulated data and real datasets, and the results demonstrate its effective performance. Additionally, the proposed method was compared with one of the existing methods in the literature, and the results indicated its superiority in terms of both classification accuracy and computational simplicity.

Goodness-of-fit Test For the Arithmetic Reduction of Age Model Based on Information Measures

Hadi Alizadeh Noughabi

In today’s industrial world, effective maintenance plays a key role in reducing costs and improving productivity. This paper introduces goodness-of-fit tests based on information measures, including entropy, extropy, and varentropy, to evaluate the type of repair in repairable systems. Using system age data after repair, the tests examine the adequacy of the arithmetic reduction of age model of order 1. The power of the proposed tests is compared with classical tests based on martingale residuals and the probability integral transform. Simulation results show that the proposed tests perform better in identifying imperfect repair models. Their application to real data on vehicle failures also indicates that this model provides a good fit.

Introducing the E_r/M/3 Queuing Model and a New (E^2-Bayesian) Estimate for Its Traffic Intensity Parameter

Shahram Yaghoobzadeh

Studying various models in queueing theory is essential for improving the efficiency of queueing systems. In this paper, from the family of models {E_r/M/c; r,c in N}, the E_r/M/3 model is introduced, and quantities such as the distribution of the number of customers in the system, the average number of customers in the queue and in the system, and the average waiting time in the queue and in the system for a single customer are obtained. Given the crucial role of the traffic intensity parameter in performance evaluation criteria of queueing systems, this parameter is estimated using Bayesian, E‑Bayesian, and hierarchical Bayesian methods under the general entropy loss function and based on the system’s stopping time. Furthermore, based on the E‑Bayesian estimator, a new estimator for the traffic intensity parameter is proposed, referred to in this paper as the E^2‑Bayesian estimator. Accordingly, among the Bayesian, E‑Bayesian, hierarchical Bayesian, and the new estimator, the one that minimizes the average waiting time in the customer queue is considered the optimal estimator for the traffic intensity parameter in this paper. Finally, through Monte Carlo simulation and using a real dataset, the superiority of the proposed estimator over the other mentioned estimators is demonstrated.