Pakistan Journal of Statistics and Operation Research
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A discrete claims-model for the inflated and over-dispersed automobile claims frequencies data: Applications and actuarial risk analysis
No full textThis paper showcases the effectiveness of the discrete generalized Burr-Hatke distribution in analyzing insurance claims data, specifically focusing on scenarios with over-dispersed and zero-inflated claims. Key contributions include presenting foundational statistical theories with mathematical proofs to enrich the paper’s mathematical and statistical aspects. Through the application of this discrete distribution, the study conducted a thorough risk analysis across five diverse sets of insurance claims data, evaluating critical risk indicators at specified quantiles. These indicators provided detailed insights into potential losses across different risk levels, supporting effective risk management strategies. The research emphasizes the importance of selecting appropriate probability distributions when analyzing zero-inflated data, as commonly observed in insurance claims. The discrete distribution accommodated these unique data characteristics and facilitated a robust analysis of risk metrics, enhancing the accuracy of potential loss assessments and reducing associated uncertainties. Furthermore, the study highlights the practical relevance of the discrete distribution in addressing specific challenges inherent to insurance claims data. By leveraging this distribution, insurers and risk analysts can improve their risk modeling capabilities, leading to more informed decision-making and enhanced financial exposure management
A Multiplicative Bias Correction Technique for Estimating Quantile Function with an Application
No full textSmooth non-parametric quantile function estimators on basis of symmetric kernels exhibit boundary bias due to spill-over near the edges. An improved non-parametric estimator of a quantile function under simple random sampling without replacement is proposed, based on a multiplicative bias corrected distribution function. There is no spill-over around the edges with our new quantile estimator. The proposed quantile estimator's asymptotic properties are investigated. The suggested method is compared to existing estimators using real data set findings, demonstrating the improved performance
A New Two-Parameters Lindley-Frailty Model: Censored and Uncensored Schemes under Different Baseline Models: Applications, Assessments, Censored and Uncensored Validation Testing
No full textClassical survival models assume homogeneity among the population of individuals who are susceptible to the event of interest. However, in many practical circumstances, there is a certain amount of unobserved heterogeneity that can be caused by a variety of sources, such as environmental or genetic factors. If the heterogeneity is ignored, many issues could arise, including an overestimation of the hazard rate and inaccurate estimates of the regression coefficients. Frailty models are usually used to model the heterogeneity among individuals. In this paper, we propose a novel univariate frailty model. The frailty variable is assumed to follow the Two Parameter Lindley distribution. The maximum likelihood method is used to estimate the model parameters. The baseline hazard functions are assumed to follow Weibull, Exponential, Gompertz, and Pareto distributions, and a simulation study is performed under this assumption. We examine the characteristics of the distribution and assess its performance compared to other distributions that are frequently applied in frailty modeling by using both Nikulin-Rao-Robson and Bagdonavicius-Nikulin goodness-of-fit tests to determine the adequacy of the model. We analyze a fresh medical dataset collected from an emergency hospital in Algeria to evaluate the effectiveness and applicability of the proposed model. 
Robust parameter estimation for one-inflated positive Poisson Lindley distribution under the presence and absence of outliers with applications to crime data
No full textThe 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
Gamma Lindley distribution in acceptance sampling plans in terms of truncated life tests with an application to industrial data
No full textAcceptance 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
Censored and Uncensored Nikulin-Rao-Robson Distributional Validation: Characterizations, Classical and Bayesian estimation with Censored and Uncensored Applications
No full textIn our paper, we introduce a novel extension of the Lomax distribution, aiming to enhance its applicability in various contexts. We emphasize a pragmatic approach in deriving mathematical properties of the new distribution, prioritizing its practical implications. Three distinct methods for characterizing the distribution are thoroughly discussed to provide a comprehensive understanding. The parameters of this newly proposed distribution are estimated through a diverse set of classical methodologies as well as Bayes’ method. Additionally, we develop the censored case maximum likelihood method to address scenarios where data may be incomplete. We meticulously compare the efficacy of likelihood estimation and Bayesian estimation using Pitman’s proximity criterion, thereby offering insights into their relative performance. For Bayesian estimation, we employ three distinct loss functions: the generalized quadratic, the Linex, and the entropy functions, each offering unique perspectives on the estimation process. Through extensive simulation experiments, we meticulously evaluate the performance of all estimation methods under various conditions, providing valuable insights into their practical utility. Furthermore, we conduct a comparative analysis between the Bayesian technique and the censored maximum likelihood method using the BB algorithm, facilitating a nuanced understanding of their respective strengths and weaknesses. In addition to estimation methodologies, we delve into the construction of the Nikulin-Rao-Robson statistic for the new model under both uncensored and censored cases. Detailed simulation studies and the presentation of two real-world applications elucidate the practical significance of our proposed statistics in diverse scenarios. Overall, our paper not only introduces a novel extension of the Lomax distribution but also provides a comprehensive exploration of various estimation techniques and statistical measures, underpinning its practical relevance across different domains
Weighted Grouping Estimation Method for Fitting Multiple Structural Regression Model when all Variables are Subject to Errors
No full textThe 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
The Topp-Leone-Gompertz-G Power Series Class of Distributions with Applications: Topp-Leone-Gompertz-G Power Series Class of Distributions
No full textA new generalized class of distributions called the Topp-Leone-Gompertz-G Power Series (TL-Gom-GPS) distribution is presented. Some mathematical and statistical properties of the new class of distributions are explored. For this new class of distributions, we derived the quantile function, moments and generating function, probability weighted moments, distribution of the order statistics and R\'enyi entropy. The maximum likelihood technique is used for estimating model parameters and Monte Carlo simulation is conducted to show the performance of the proposed model. Finally, the usefulness and flexibility of the new class of distributions is examined by means of applications to real data sets
Using the Single-Exponential-Smoothing Time Series Model under the Additive Holt-Winters Algorithm with Decomposition and Residual Analysis to Forecast the Reinsurance-Revenues Dataset
No full textTime series analysis plays a pivotal role in the strategic planning and risk management of reinsurance companies. It is an indispensable tool for gaining insights into the future utilization of reinsurance revenues. To effectively safeguard against substantial financial losses stemming from anticipated claims, reinsurance businesses must have a thorough understanding of the expected values of these claims. The ability to estimate the potential value of future claims is paramount, as it empowers reinsurance companies to proactively prepare and allocate resources, ensuring that they are well-equipped to cover likely future claims. Our research incorporates an innovative approach to estimate reinsurance revenues, leveraging the power of time series analysis. By applying the proposed paradigm to an original time series dataset, we aim to showcase its practical value and effectiveness in predicting future revenue trends. To assess the accuracy of these predictions, we employ the Box-Ljung statistical test, a statistical test commonly used in time series analysis. The corresponding p-value generated from this test provides a quantitative measure of the ability to analyze, capture and explain the underlying patterns in the data, thereby aiding reinsurance companies in providing an informed decisions and managing their financial risks effectively. In summary, the integration of time series analysis, single exponential smoothing (SEXS), and advanced forecasting techniques forms a critical foundation for enhancing the predictive capabilities of reinsurance businesses and ensuring their financial stability in the face of uncertain future claims
A Novel Model for Finance and Reliability Applications: Theory, Practices and Financial Peaks Over a Random Threshold Value-at-Risk Analysis
No full textIn 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