Journal of Statistical Modelling: Theory and Applications
Volume:2 Issue: 2, Summer and Autumn 2021

The Maxwell-Dagum distribution is a continuous statistical distribution suitable for modeling data sets relating to various fields including finance, business, medical sciences, survival analysis, and related areas. This article aimed to propose some important properties of the Maxwell-Dagum distribution and obtained the parameters of its estimates by using different methods of estimation including maximum likelihood estimation, the maximum product of spacings, least squares estimation, and weighted least squares estimation. The first and second derivatives of this distribution are studied. We present two real data sets relating to the COVID-19 mortality rate belonging to Canada and the waiting time of bank customers to assess the performance  of the proposed distribution. It is discovered that the Maxwell-Dagum distribution can be chosen as the best distribution by having a minimum value of Akaike information and Bayesian information criteria.

In this paper, we apply the inverse trinomial distribution with parameters (p, q, λ) to count data exhibiting over-dispersion. We compare results for the mean parameterized inverse trinomial and the parameter λ as linear predictors in the generalized linear model case. Our results also demonstrate methods for obtaining the means and variances for the zero-inflated and zero-truncated inverse trinomial distributions. Results obtained here indicate that the generalized Poisson type II has a close relationship with the inverse trinomial distributions. Several data examples are employed in this paper for both frequency and data having covariates cases. SAS PROC NLMIXED is employed using adaptive Gaussian quadrature and the Newton-Raphson as the optimizer.

Generalized extreme value regression is often more adapted when we investigate a relationship between a binary response variable that represents a rare event and potential predictors. In particular, we use the quantile function of the generalized extreme value distribution as the link function. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, hypotheses testing) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimator by measuring those properties when sampling from an approximating distribution. In this paper, we fit the generalized extreme value regression model and perform a parametric bootstrap method for testing hypotheses and confidence interval estimation of parameters for the generalized extreme value regression model with a real data application.

In this article, the autoregressive model of order one with exponential innovations is considered. The maximum likelihood and Bayes estimators of the autoregression parameter, under squared error loss function with non-informative prior are examined. A simulation study is conducted to compare the behavior of the estimators via their relative bias and risks. Moreover, a real data example is presented.

The present study proposes several methods for improving the parameter estimation of interval-censored exponential lifetime data. These methods can be regarded as the versions of substitution method which are based on the most probable time of occurring failures or the meantime of failures in each inspection interval. Based on simulation studies, the methods proposed in this present study can improve the existing estimators which are based on the midpoint of inspection intervals “or” the exponential probability plot.

A new generalized distribution called the gamma odd power generalized Weibull-G family of distributions is developed and studied. Some special models of the new family of distribution are explored. Statistical properties of the new family of distributions including the quantile function, ordinary and incomplete moments, probability weighted moments, stochastic ordering, distribution of the order statistics, and Rényi entropy are presented. The maximum likelihood method is used for estimating model parameters, and Monte Carlo simulation is conducted to examine the performance of the model. The flexibility of the new family of distributions is demonstrated by means of two applications to real data sets.

Missing data is a very common problem in all research fields. Case deletion is a simple way to handle incomplete data sets which could mislead to biased statistical results. A more reliable approach to handle missing values is imputation which allows covariate-dependent missing mechanism, as well. This paper aims to prepare guidance for researchers facing missing data problems by comparing various imputation methods including machine learning techniques, to achieve better results in supervised learning tasks. A benchmark dataset has experimented and the results are compared by applying popular classifiers over varying missing mechanisms and rates on this benchmark dataset.

A new generalized family of distributions called the Weibull Odd Burr III-G is introduced using the T-X transformation technique. Some of useful mathematical and statistical properties such as the hazard function, quantile function, moments, probability weighted moments, Rényi entropy, order statistics and stochastic orders are derived. The method of maximum likelihood estimation is used to estimate the model parameters. The usefulness of these family of distributions is demonstrated via simulated experiments and its special cases are applied to real life data sets to illustrate flexibility.

The performance of justice systems is measured by empirical indicators in both developing and developed countries. The findings of existing indicator initiatives have historically been based on surveys of experts, document reviews, administrative data, or public surveys. In this paper, Principal Component Analysis (PCA) and Cluster Analysis (CA) methods were combined to resolve the problem of evaluating multiple indicators. Using PCA, this method standardizes, reduces dimensions, and decorrelates multiple indicators of evaluation of justice systems and abstracts the principal components. Then, CA is used to assign individuals (observations) to homogeneous clusters (classes). Typically, hierarchical clustering on principal components (HCPC) is employed to classify civil branches of a trial court in Iran to create a comprehensive evaluation. By applying the multivariate statistical method to data, three principal components are identified and interpreted. A hierarchical clustering algorithm is then applied, which divides the data into three clusters based on dissimilarity. These groups of the civil branches were identified based on nine judicial performance indicators. It allows policymakers and reformers to measure the performance of each branch individually, and track their progress in reducing backlogs and delays separately. As shown by the practical example, these methods are effective across justice units