Journal of Statistical Modelling: Theory and Applications
Volume:4 Issue: 1, Winter and Spring 2023

Moments play an essential role in the characterization of statistical distributions and criteria such as dispersion‎, ‎skewness‎, ‎and kurtosis‎. ‎This article is a dissection of the central moments of two-point and binomial distributions‎. ‎First‎, ‎we consider the Bernoulli distribution of the population and generalize the results‎. ‎With a simple method‎, ‎we present the condition that when the sample size is large‎, ‎the structure of the sample central moment consists of random variables independent of standard normal or chi-square or a combination of both‎. ‎In the obtained results‎, ‎the role of points that have a probability of 1/2 is very influential in the limit distribution.‎

Suicide is a complex issue that affects many regions globally‎, ‎and the factors that contribute to it can differ based on geographical and cultural contexts‎. ‎In this study‎, ‎we examine the relationship between socioeconomic factors and suicide mortality rates across 31 provinces in Iran‎, ‎using data from 2020‎. ‎We employ spatial econometric methods to analyze the data‎, ‎allowing us to explore the statistical relationships between economic models and regional science‎. ‎Our analysis reveals a significant clustering of suicide mortality in some western provinces‎, ‎as shown by the distribution map of suicide mortality by province‎. ‎We also find that the unemployment rate has a significant impact on suicide mortality‎. ‎These findings provide valuable information for developing effective prevention strategies.

In this paper‎, ‎we propose a unit distribution called the logit Gudermannian distribution and present various statistical properties of the proposed model‎. ‎Six parameter estimation methods are explored in the quest to estimate the parameters of the proposed distribution‎. ‎We determine which estimation methods provide better parameter estimates through simulation studies‎. ‎The study shows that the logit Gudermannian distribution provides a better fit for the datasets used than other unit distributions‎. ‎Consequently‎, ‎the logit Gudermannian distribution is used to develop a parametric regression model for studying the relationship between a unit response variable and other exogenous variables‎. ‎The new regression model's performance is compared to that of other existing regression models and found to be competitive.

In the real world‎, ‎we may come across with zero-inflated or zero-deflated count data that have a very short-run autocorrelation‎. ‎Integer-valued moving average processes are suitable for modeling these data‎. ‎In this paper‎, ‎a non-negative integer-valued moving average process of the first order with zero-modified geometric innovations is introduced‎. ‎This model is called zero-modified geometric INMA(1) process which contains geometric INMA(1) process ‎as a particular case‎. ‎Some statistical properties of the process are obtained‎. ‎The parameters of the model are estimated by the Yule-Walker method‎. ‎Then‎, ‎using the simulation study‎, ‎we evaluate the performance of this estimators‎. ‎Finally‎, ‎the model is applied to two examples of real time series of the monthly number of rubella cases and the annually number of earthquakes magnitude 8.0 to 9.9‎. ‎Then‎, ‎we exhibit the ability of the model for fitting and predicting count data with excess and deficit of zeros.

Nonlinear regression models have widespread applications across diverse scientific disciplines‎. ‎Achieving precise fitting of the optimal nonlinear model is essential‎, ‎taking into account the biases inherent in Bayesian optimal design‎. ‎This study introduces a Bayesian optimal design utilizing the Dirichlet process as a prior‎. ‎The Dirichlet process is a fundamental tool in exploring Nonparametric Bayesian inference‎, ‎providing multiple well-suited representations‎. ‎The research paper presents a novel one-parameter model‎, ‎termed the ``unit-exponential distribution"‎, ‎specifically designed for the unit interval‎. ‎Additionally‎, ‎a representation is employed to approximate the D-optimality criterion‎, ‎considering the Dirichlet process as a functional tool‎. ‎Through this approach‎, ‎the aim is to identify a nonparametric Bayesian optimal design.

This paper describes the point and interval estimation of the unknown parameters of modified Weibull distribution under the adaptive Type-II progressive censored samples‎. ‎First‎, ‎we obtain the maximum likelihood estimation of parameters‎. ‎Because maximum likelihood estimations should be solved in numerical methods and cannot be derived in a closed form‎, ‎the approximate maximum likelihood estimations of the parameters are achieved‎. ‎Also‎, ‎asymptotic confidence intervals are obtained by earning the asymptotic distribution of the parameters‎. ‎Moreover‎, ‎two bootstrap confidence intervals are derived‎. ‎Second‎, ‎the Bayesian estimation of parameters is approximated using the Markov chain Monte Carlo algorithm and Lindley's method‎. ‎Furthermore‎, ‎the highest posterior density credible intervals of the parameters are derived‎. ‎Finally‎, ‎the different proposed estimations have been compared by the simulation studies and one data set is analyzed to illustrative aims.

This study focuses on estimating the reliability of a multicomponent stress-strength model using two Bayesian approaches‎: ‎E-Bayesian and hierarchical Bayesian‎. ‎This model follows Inverse Rayleigh distributions with distinct parameters‎. ‎Additionally‎, ‎the efficiency of the proposed methods is compared by employing Monte Carlo simulation and analyzing a data set.

Often‎, ‎reliability systems suffer shocks from external stress factors‎, ‎stressing the system at random‎. ‎These random shocks may have non-ignorable effects on the reliability of the system‎. ‎In this paper‎, ‎we provide sufficient and necessary conditions on components' lifetimes and their survival probabilities from random shocks for comparing the lifetimes of two fail-safe systems in two cases‎: ‎(i) when components are independent‎, ‎and then (ii) when components are dependent‎. ‎We then apply the results for some distribution-free random variables with possibly different parameters to illustrate the established results.

For the interference models‎, ‎the assumption is often made that the size of the blocks (k) is not greater than the number of treatments (t)‎. ‎Typically‎, ‎it is difficult to specify optimal block designs theoretically or algorithmically when k> t. ‎In this article‎, ‎we focus on a one-sided interference model with compound symmetry correlation for the observations and obtain universally optimal block designs for both cases k≤ t and k>t. ‎We present some methods for constructing these optimal designs for various numbers of treatments and block sizes.

Spatial data analysis methods have many applications in various fields‎, ‎such as agriculture‎, ‎mining engineering‎, ‎and meteorology‎. ‎In this study‎, ‎ordinary kriging and indicator kriging are considered to predict alumina grade in the Jajarm mine in Iran‎, ‎and the precision of the methods is computed‎. ‎A conditional simulation is carried out based on the data set for a more general comparison of ordinary and indicator kriging to interpolate Alumina grade in the mine‎. ‎In the case of monitoring possible variation related to sample size and type of variogram model‎, ‎simulations are performed with various sample sizes and different types of variogram models‎. ‎Then ordinary and indicator kriging methods are applied for every set of simulated data (concerning different sample sizes and types of variogram models)‎, ‎and root of standardized mean square error prediction is considered as a cross-validation criterion to compare the kriging methods‎. ‎The simulation results show that under the assumptions‎, ‎ordinary kriging has better performance than the indicator kriging method.

Most of the research on optimal designs concentrates on D-optimal designs for linear and nonlinear models with fixed effects‎. ‎Recently nonlinear models with random effects have been of great attention because these models are more applicable to describing real data‎. ‎In this paper‎, ‎E-optimal designs for the Poisson regression with random effects have been considered‎. ‎A new version of the equivalence theorem is prepared for this criterion in the Poisson regression model with random effects.

In this paper‎, ‎we develop a version of the weighted Marshall-Olkin bivariate exponential model by incorporating a new parameter‎. ‎This parameter describes the dependence structure between margins via a copula function‎. ‎We choose the inference for margins method to estimate the model parameters along with the copula parameter‎, ‎as this method offers more advantages than the maximum likelihood estimation method‎. ‎Additionally‎, ‎we conduct a comprehensive simulation study to investigate the behavior of the copula parameter estimator and the remaining parameters‎. ‎Finally‎, ‎an analysis of a real dataset on automobile insurance reveals that the Clayton copula characterizes the dependence structure within the Archimedean copula family