Journal of Statistical Sciences

Application of Extropy in Characterization of Some Continuous Distributions

Masoumeh Akbari

In this paper, quantile-based dynamic cumulative residual and failure extropy measures are introduced. For a presentation of their applications, first, by using the simulation technique, a suitable estimator is selected to estimate these measures from among different estimators. Then, based on the equality of two extropy measures in terms of order statistics, symmetric continuous distributions are characterized. In this regard, a measure of deviation from symmetry is introduced and how it is applied is expressed in a real example. Also, among the common continuous distributions, the generalized Pareto distribution and as a result the exponential distribution are characterized, and based on the obtained results, the exponentiality criterion of a distribution is proposed.

Optimal Ruin Probabilities in the Excess Loss Reinsurance Model

Abouzar Bazyari

In the excess loss reinsurance risk model, the amount of insurance premium paid by the company is influential in the ruin of that company. In this paper, the premium function is presented based on the expected amount of total payments of the reinsurer to the assigning insurer, the constraint on this function is investigated, and for the claims with any arbitrary distribution, the contour plots are drawn and with presenting optimization algorithm, infinite time ruin probability function will be minimum for different values of initial capital and threshold value. Finally, the excess loss reinsurance risk model with non-exponential claims is considered, and the infinite time ruin probability is calculated with numerical examples.

Asymptotic Distribution of ُSome Statistics in Multivariate Inference Based on Taylor Series Expansion

Sakineh Dehghan

The exact distribution of many applicable statistics could not be accessible in various statistical inference problems. To deal with such an issue in the large sample problem, an approach is to obtain the asymptotic distribution. In this article, we have expressed the asymptotic distribution of multivariate statistics class approximated by averages based on the Taylor expansion. Then, the asymptotic distribution of an empirical Mahalanobis depth-based statistic is obtained, and the statistic is applied to test the scale difference between two multivariate distributions. Simulation studies are carried out to explore the behavior of the asymptotic distribution of the test statistic. A real data example illustrating the use of the test is also presented.

Reliability Estimation of the Stress-Strength Model in Coherent Systems Based on Exponential Distribution

ali rostami

This article considers the stress-strength reliability of a coherent system in the state of stress at the component level. The coherent series, parallel and radar systems are investigated. For 2-component series or parallel systems and radar systems, this reliability based on Exponential distribution is estimated by maximum likelihood, uniformly minimum variance unbiased and Bayes methods. Also, simulation studies have been done to check estimators' performance, and real data are analyzed.

Analysis of High Dimensional Data Using Development Support Vector Regression, Functional Regression, Ridge and Lasso Regression

Mahdi Roozbeh

‎The high-dimensional data analysis using classical regression approaches is not applicable, and the consequences may need to be more accurate.
This study tried to analyze such data by introducing new and powerful approaches such as support vector regression, functional regression, LASSO and ridge regression. On this subject, by investigating two high-dimensional data sets (riboflavin and simulated data sets) using the suggested approaches, it is progressed to derive the most efficient model based on three criteria (correlation squared, mean squared error and mean absolute error percentage deviation) according to the type of data.

A Different Attitude in Analyzing $3$-Way Contingency Tables Using Conditional Independence

Me'raj Abdi

This paper proposes a different attitude for analyzing three-way contingency tables using conditional independence. We show that different types of independence explored in log-linear models can be achieved without using these models and only by using conditional independence. Some numerical examples are presented to illustrate the proposed methods.

Response Surface Method in the Presence of Uncontrollable Factors

Mehdi Kiani

In the 1980s, Genichi Taguchi, a Japanese quality advisor, claimed that most of the variability affiliated with the response could be attributed to the company of unmanageable (noise) factors. In some practical cases, his modeling proposition evidence leads the quality improvement to many runs in a crossed array. Hence, several researchers have em-braced noteworthy attitudes of response surface methodology along with the robust parameter design action as alternatives to Taguchi's plan. These alternatives model the response's mean and variance corresponding to the combination of control and noise factors in a combined array to accomplish a robust process or production. Indeed, using response surface methods to the robust parameter design minimises the impression of noise factors on assembling processes or productions. This paper intends to develop further modeling of the predicted response and variance in the presence of noise factors based on unbiased and robust estimators. Another goal is to design the experiments according to the optimal designs to improve these estimators' accuracy and precision simultaneously.

A Criterion for Assessment of Search Designs in Robust Parameter Experiments

Mohsen Motavaze

Production of high-quality products necessitates identifying the most influential factors, among many factors, for controlling and reducing quality variation. In such a setting, the factorial designs are utilized to determine the active factors with maximal information and model an appropriate relation between the factors and the variable of interest. In this regard, robust parameter designs dividing the factors to control- and noise factors are efficient methods for offline quality control for stabilizing the quality variation in the presence of the noise factors. Interestingly, this could be achieved through exploiting active control by noise interactions. One needs to experiment with numerous treatments to detect the active interaction effects. Search designs are suggested to save treatments, and a superior one is recommended among the appropriate ones. To determine the superior design, one needs a design criterion; however, the existing criteria could be more beneficial for robust parameter designs. In this paper, we proposed a criterion to rank the search designs and determine the superior one.

On Some Reliability Concepts in Fuzzy Environment

Mohammad Khanjari Sadegh

In this paper, some reliability concepts have been investigated based on the α-pessimistic and its relationship with the α-cut of a fuzzy number. For this purpose, if the lifetime distribution of the system components is known, using the definition of the scale fuzzy random variable, based on α-pessimistic, some reliability criteria have been investigated. Also, suppose the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the features are available. In that case, the empirical distribution function of the fuzzy data is used to estimate the reliability, and some examples are provided to illustrate the results.

Improving Fellegi-Sunter ‎model in record linkage using log-linear model and weight ‎adjustment ‎

Zahra Rezaei Ghahroodi

‎T‎oday, with the increasing access to administrative databases and the high volume of data registered in organizations, the traditional methods of data collection and analysis are not effective due to the response burden. Accordingly, the transition from traditional ‎survey methods to modern methods of data collection and analysis with the register-based statistics approach has received more and more attention from statistical data analysts. In register-based methods, it is especially important to create an integrated database by linking database records of different organizations. ‎Many record linkage algorithms have been developed using the Fellegi and Sunter ‎‎‎model‎. ‎The Fellegi-Sunter model does not leverage information contained in field values and does not care about specific possible values of a string variable (more common and less common values)‎. ‎In this ‎‏‎article‎, ‎a method that can be able to infuse these differences in specific possible values of a string variable in the Fellegi-Sunter model is presented‎.‎ ‎‎‎On the ‎other, ‎‎the ‎‎model proposed by Fellegi-Sunter‎, ‎as well as the method for adjusting the matching weights in the frequency-based record linkage‎, ‎binding in this paper, ‎are based on the assumption of conditional independence‎. ‎In some applications of record linkage‎, ‎this assumption is not met in agreement or disagreement of common variables which are used for matching‎. ‎One solution used in such a case is to use log-linear model which allows interactions between matching variables in the model‎.‎‎

In this ‎‏‎article‎, ‎we deal with two generalizations of Fellegi-Sunter ‎‎‎‎‎model, ‎one with the correction of the matching weights and the other with using a log-linear model with interactions in absence of conditional independence‎. ‎The proposed methods are implemented on labour force data set of Statistical Centre of Iran using R‎.

A Permutation Test for Multiple Correlation Coefficient in High Dimensional Normal Data

Dariush Najarzadeh

In multiple regression analysis, the population multiple correlation coefficient (PMCC) is widely used to measure the correlation between a variable and a set of variables. To evaluate the existence or non-existence of this type of correlation, testing the hypothesis of zero PMCC can be very useful. In high-dimensional data, due to the singularity of the sample covariance matrix, traditional testing procedures to test this hypothesis lose their applicability. A simple test statistic was proposed for zero PMCC based on a plug-in estimator of the sample covariance matrix inverse. Then, a permutation test was constructed based on the proposed test statistic to test the null hypothesis. A simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets. This study was finally ended by applying the proposed approach to mice tumour volumes data.

Estimation of Traffic Intensity Parameter and Stationarity Probability of M/M/c Queuing System Under a Stop Time in the System

Shahram Yaghoobzadeh

In this article, it is assumed that the arrival rate of customers to the queuing system M/M/c has an exponential distribution with parameter $lambda$ and the service rate of customers has an exponential distribution with parameter $mu$ and is independent of the arrive rate. It is also assumed that the system is active until time T. Under this stopping time, maximum likelihood estimation and bayesian estimation under general entropy loss functions and weighted error square, as well as under-informed and uninformed prior distributions, the system traffic intensity parameter M/M/c and system stationarity probability are obtained. Then the obtained estimators are compared by Monte Carlo simulation and a numerical example to determine the most suitable estimator.