Pakistan Journal of Statistics and Operation Research

Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data

Razik Ridzuan Mohd Tajuddin, Muhammad Aslam Mohd Safari, Noriszura Ismail — Fri, 06 Sep 2024 21:54:48 +0500

The one-inflated positive Poisson Lindley model has been recently introduced as an alternative in modelling positive count data with a large number of ones: a phenomenon known as one-inflation. In the presence of one-inflation, this model has a high tendency to be influenced by outliers, making usual parameter estimations to be less robust. Hence, several estimators: maximum likelihood, method of moments, ordinary least squares, weighted least squares, Cramér-Von Mises, modified Cramér-Von Mises (MCVM) and maximum product of spacing (MPS); for the parameters of the model are also proposed and investigated in terms of unbiasedness, consistency and joint efficiency under the presence and absence of outliers. When the outliers are absent, the MPS estimator is the best estimator and when the outliers are present, the MCVM estimator is the best estimator. Model fittings to two real datasets with one-inflation and outliers support the simulation results and conclude that the MCVM estimator is the best estimator. Based on the best robust estimator, the population size of the number of offenders as well as the likelihood of arrests were estimated.

A New Pareto Model: Risk Application, Reliability MOOP and PORT Value-at-Risk Analysis

Fri, 06 Sep 2024 21:57:50 +0500

The paper introduces a new reliability Burr Pareto type-II model, showcasing its versatility and effectiveness in engineering applications, particularly in analyzing the failure and service times of aircraft windshields. The BUPII model's application in failure analysis offers insights into the probabilistic behavior of windshield failures, aiding in risk prediction and management. Similarly, its extension to service time analysis demonstrates its utility in optimizing maintenance schedules and operational efficiency. Moreover, the paper conducts a rigorous mean-of-order P analysis under both failure and service time datasets, validating the new model's reliability assessment capabilities. Furthermore, employing the peaks over random threshold value at risk analysis highlights the model's practical relevance in quantifying financial risks associated with extreme events. Overall, the novel probability distribution emerges as a valuable tool for engineers and researchers involved in reliability and risk analysis, promising advancements in understanding and managing the reliability of engineering systems. Future research could explore broader applications and refined methodologies to further enhance predictive capabilities and decision-making support.

Generalized Exponential Ratio Type Estimator for the Finite Population Mean Under Ranked Set Sampling

Khalid ul Islam RATHER, Eda Gizem KOÇYİĞİT — Fri, 06 Sep 2024 22:08:06 +0500

In this study, we introduce a novel approach for estimating the mean of a finite population using Ranked Set Sampling (RSS), termed the generalized exponential ratio estimator. We derive expressions for the bias and mean squared error (MSE) of the proposed estimator up to the first order of approximation. To assess its performance, we conduct a thorough theoretical and numerical analysis using simulated and real data. Our results demonstrate that the generalized exponential ratio estimator outperforms both the classical ratio estimator and the estimator proposed by Kadilar et al. (2009) under RSS, highlighting its superior efficiency.

A Novel Robust Class of Estimators for Estimation of Finite Population Mean: A Simulation Study

Muhammad Abid, Sun Mei, Waqas Latif, Tahir Nawaz — Sat, 07 Sep 2024 15:24:36 +0500

In the existing survey sampling literature, the ratio-type estimators are an obvious choice to estimate the finite population mean when auxiliary information related to the study variable is readily available. Typically, auxiliary information is incorporated into ratio-type estimators by using conventional measures such as mean, range, coefficient of kurtosis, coefficient of skewness and coefficient of correlation, etc. which are less efficient when extreme observation are present in the data. This study provides a remedy and enhances the efficiency of the ratio-type estimators of population mean in the presence of extreme observations by proposing dual auxiliary variables based exponential-cum-ratio class of estimators which integrates both conventional and non-conventional measures under simple random sampling without replacement. The expression of the mean squared error and theoretical efficiency conditions for proposed class of estimators have been obtained for comparison purposes. A simulation study was carried out based on contaminated normal distribution and the robustness of the proposed estimators has been assessed in the presence of extreme observations. For practical implementation, six real data sets have been used to compare the performance of the proposed estimators with competing estimators to support the theoretical results. The theoretical and empirical results suggest that the proposed estimators are more precise than usual mean as well as existing estimators’ ratio-type considered in this study.

Detection of Outliers Method in Grouped Multivariate Data: A Method Based on Multiple Linear Regression

Suthat Phuttisen , Wuttichai Srisodaphol — Sat, 07 Sep 2024 15:25:54 +0500

Cluster analysis is applied to group data so that samples within the same group are similar. A common problem with multivariate data implementation is that the data differs significantly from most of the other data. Outliers can significantly impact data analysis and model performance, making their detection crucial in various domains. This study presents an investigation of the outlier detection method using multiple linear regression for grouped multivariate data. The research compares the performance of the proposed method with two existing approaches, namely the Caroni and Billor (2007) method and the Hardin and Rocke (2004) method. In the case of uncontaminated data, the proposed method demonstrates a high percentage of detected outliers as the number of variables and sample size increase, indicating its effectiveness in outlier identification. In the scenario of contaminated data, the results reveal that the proposed method consistently outperforms both the Caroni and Billor method and the Hardin and Rocke method in terms of accuracy and precision. These findings highlight the effectiveness of the proposed method for outlier detection in grouped multivariate data. The study contributes to the existing knowledge of outlier detection approaches and provides insights into their performance under different data conditions. Researchers and practitioners can benefit from these findings when selecting appropriate outlier detection methods for various applications.

Gamma Lindley distribution in acceptance sampling plans in terms of truncated life tests with an application to industrial data

Amer Ibrahim Al-Omari, Mohd Ismail — Sat, 07 Sep 2024 15:27:24 +0500

Acceptance sampling plans (ASP) are needed in areas where 100% inspection is impractical or expensive. They help ensure product quality meets requirements, reduce inspection costs, and prevent nonconforming goods from reaching customers. The ASP that are well-planned offer an efficient and dependable way to maintain quality control in manufacturing procedures and supply chains. The Gamma Lindley distribution (GaLD) is used to design acceptance sampling plans in this study when the life test is truncated at a pre-specified (pre-determined) time. The mean is used as the quality parameter. The smallest sample size is required to guarantee that the desired life mean is reached at the risk of the particular consumer. In addition to the producer's risk, the operating characteristic values of the sample plans are presented. In order to evaluate the suggested sampling plans, a real data from the first failure of 20 electric carts utilized for internal transportation and delivery in a big manufacturing facility is provided.

Weighted Grouping Estimation Method for Fitting Multiple Structural Regression Model when all Variables are Subject to Errors

Ro'ya Al Dibi'i, Rosmanjawati Abdul Rahman, Amjad Al-Nasser — Sat, 07 Sep 2024 15:30:20 +0500

The Measurement Error Model (MEM) is employed to fit the relationship between two or more variables when all variables are subject to measurement errors. In the specific case of only two variables, this model is referred to as the Error in Variables model. This paper proposes two new estimation methods for a multiple structural measurement error model, applicable when all variables are subject to errors. The proposed methods, the Repetitive Weighted Grouping and the Iterative Weighted Grouping, are extensions of the Wald estimation method. To evaluate the performance of these new estimators compared to classical estimators-namely, the Maximum Likelihood Estimator (MLE) and the Method of Moments (MOM), a Monte Carlo experiment was conducted. The simulation results showed that the proposed estimators outperform the classical estimators in terms of root mean square error and bias. Additionally, real data analysis was performed to assess the relationships between national GDP, unemployment rate, and human development index using the proposed estimation methods. The results reveal that, based on mean square error (MSE), the proposed methods with r =3 and r =4 yield more accurate estimators than other methods in weight case 1, while the proposed method with r =4 proves more accurate in weight case 2. Furthermore, the proposed procedures demonstrate greater efficient than MLE and MOM in fitting the model.

A Novel Model for Finance and Reliability Applications: Theory, Practices and Financial Peaks Over a Random Threshold Value-at-Risk Analysis

Abdussalam Aljadani, Mahmoud M. Mansour, Haitham M. Yousof — Sat, 07 Sep 2024 15:31:33 +0500

In this paper, the authors introduce a new three-parameter lifetime probability distribution known as the Marshall-Olkin-generated log-logistic (LL) distribution. They thoroughly examine and describe this distribution, providing insights into its characteristics and its suitability for various applications. This newly constructed distribution's density function exhibits characteristics of both symmetry and right-skewness, providing modelling flexibility across a range of datasets. Because of its skewness coefficient, which can take both positive and negative values, a wide range of data asymmetries can be represented. The Marshall-Olkin generated LL distribution's corresponding hazard rate displays a variety of characteristics, including monotonic increase, increasing-constant, constant, upside-down, and monotonic drop. Because of its adaptability, the distribution can successfully capture various risk or failure rate patterns across time. Using a number of techniques, the researchers expand this distribution to the bivariate domain. Its utility in modelling multivariate lifetime data and inter-variable relationships is improved by these extensions. The researchers use the maximum likelihood method to estimate the parameters of the distribution, which ensures reliable and effective parameter estimation from observed data. They carry out an extensive simulation research to analyse biases and mean squared errors in a range of scenarios and sample sizes in order to evaluate the finite behaviour of the maximum likelihood estimators. In real-life and reliability applications, this meticulous methodology aids in evaluating the estimators' precision and dependability. Because it may offer a comprehensive and nuanced knowledge of high financial risks, the Peaks Over a Random Threshold Value-at-Risk (PORT-VaR) study is crucial for evaluating Norwegian fire insurance claims. This financial analysis is given extra consideration.

On estimation and monitoring of population mean using systematic sampling under an exponentially weighted moving average scheme

Amber Karim, Hina Khan, Yasar Mahmood, Muhammad Riaz, Shabbir Ahmad — Sat, 07 Sep 2024 15:39:59 +0500

The present study proposes a generalized ratio estimator for estimating the population mean under the systematic sampling technique by considering auxiliary information and auxiliary attribute. Its bias and Mean Square Error (MSE) expressions have been derived. Mathematical comparisons are made by comparing the proposed estimator with the usual mean estimator, Swain (1964) estimator, Bhal and Tuteja (1991) estimator, and Singh and Singh (1998) estimator, and it is shown that the proposed estimator is more efficient than the previous estimators. A numerical comparison is also performed to demonstrate the superiority of the proposed estimator over the traditional estimators. The technique of ratio estimators based on systematic sampling is used to design an Exponentially Weighted Moving Average (EWMA) control chart. The Control chart is a significant industrial tool for monitoring the process mean. To evaluate performance efficiency Average run lengths (ARL) are obtained in this study. The proposed charts are compared based on out-of-control ARLs. A chart based on the proposed estimator is superior as it detects the shifts earlier than charts based on existing estimators. Empirical work is done to support the study. The suggested efficiency is further addressed utilizing real-life examples and simulations using R-Studio.

A Bimodal Extension of the Tanh Skew Normal Distribution: Properties and Applications

Sat, 07 Sep 2024 18:13:18 +0500

This article introduces a novel family of skew distributions namely Bimodal Tanh Skew Normal (BTSN)
distributions, which incorporates a new skew function with the help of hyperbolic tangent function. This
new distribution is designed to accommodate data sets with two modes. Besides, the article presents various
essential mathematical properties, such as moments, moment generating function, characteristic function,
mean deviation, characterizations and the method for maximum likelihood estimation of this distribution.
A simulation study is also conducted using Metropolis–Hastings algorithm to examine the behavior of the
obtained parameters. Furthermore, the practical utility of this new distribution is demonstrated through
a real life application involving a specific data set. To assess the suitability of the BTSN distribution, the
article employs Akaike information criterion (AIC) and Bayesian information criterion (BIC). Finally, a
likelihood ratio test is conducted to distinguish between the new model and the existing competing models.

Dependence of Drought Characteristics: Parametric and Non-parametric Copula Approach

Omer Ozan Evkaya, Hongyi Lu — Sat, 07 Sep 2024 18:15:49 +0500

Drought, which has harmful impacts both environmentally and economically, is one of the most devastating natural phenomena. In order to better understand and monitor the effects of drought, various methods have been developed in recent decades to quantify drought characteristics, with a primary focus on univariate drought indices. Mainly, drought characteristics are crucial to examine the impacts of drought in-depth on any specific area. This study endeavours to investigate univariate and bivariate drought indices using both parametric and non-parametric copula techniques. For that purpose, drought characteristics, such as duration, severity, mean intensity and peak intensity are analysed relying on different drought indices. The dependence among the main characteristics is evaluated and corresponding bivariate return period calculations are investigated. The data set used in this study is retrieved from monthly meteorological observations collected at five different Stations in Konya, located in the Central Anatolia Region of Turkey. Main numerical findings indicate the importance of using multiple drought indices for different geographical reasons for extreme dry periods.

Estimation and Analysis of Trigonometric Models under Bayesian Approach

Laxmi Prasad Sapkota, Pankaj KUMAR, Vijay Kumar, Nirajan Bam — Sat, 07 Sep 2024 18:17:01 +0500

In this study, we explore three innovative trigonometric models within the Bayesian framework, utilizing the inverse Weibull distribution as our foundation. These models—namely the Sine inverse Weibull, Cosine inverse Weibull, and Tan inverse Weibull—are crafted from distinct distribution families. We employ both maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) simulation techniques to estimate parameters, drawing upon a comprehensive dataset. By scrutinizing posterior samples numerically and graphically, we evaluate the efficacy of our models, generating Bayes estimates for parameters, examining reliability and hazard functions, and establishing credible intervals. Furthermore, we assess the predictive capacity of all three models through posterior predictive checks. We also conduct comparative analyses, pitting our models against competing ones using real-world data. Notably, our results reveal that the proposed trio of models exhibit strikingly similar performance in terms of fitting the data.