Pakistan Journal of Statistics and Operation Research
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On The Efficiency of Receiving a Stepwise Gaussian Random Disturbance With an Unknown Moment of Appearance and Central Frequency
No full textThe synthesis of the computationally simple maximum likelihood algorithms for detecting and measuring the moment of appearance and the central frequency of a fast-fluctuating Gaussian random disturbance is carried out. Using the method of multiplicative and additive local Markov approximation of the decision-determining statistics or its increment, the closed analytical expressions are found for the false alarm and missing probabilities (the detection task), as well as for the conditional biases and variances of the desired estimates (the measurement task). By statistical simulation methods, it is established that the proposed detector and measurer are operable, and the analytical formulas describing their performance are in good agreement with the corresponding experimental data in a wide range of parameter values of the random process being analyzed
Point and Interval Estimation Techniques for the 2S-Lindley Distribution Under Type-II Censoring
No full textRecently, Chesneau et al. (2020) introduced a new distribution called the 2S-Lindley distribution, which is based on the sum of two independent Lindley random variables with the same parameter. In this paper, we employ different methods to estimate the unknown parameter of the 2S-Lindley distribution using type-II censored samples. These methods include the moment-based method, maximum likelihood estimation, the bootstrap method, and Bayesian inference. We provide both point and interval estimates for the parameter using each method. We also analyze a real data set that follows the 2S-Lindley distribution, computing and comparing various estimates. Finally, we conduct a simulation study to illustrate and compare the effectiveness of these methods
Properties and Application of Trimodal Skew Normal Distribution
No full textA new type of continuous distribution that extends the skew distribution developed by Azzalini (1985) is presented in this paper. This new distribution is designed to effectively model real-life data that may have up to three modes. The primary objective of this study is to provide a comprehensive understanding of the structural properties of this distribution, including moments, moments generating function, Fisher's information matrix, characterization, and parameter estimation through the method of maximum likelihood. Additionally, the distribution's flexibility and usefulness are evaluated by analyzing two real-life datasets. The analysis findings suggest that, as measured by AIC and BIC values, the new distribution demonstrates superior performance in fitting the datasets compared to other distributions. The lower values of AIC and BIC suggest that the new distribution better fits the datasets compared to other alternatives
A Novel Insurance Claims (Revenues) Xgamma Extension: Distributional Risk Analysis Utilizing Left-Skewed Insurance Claims and Right-Skewed Reinsurance Revenues Data with Financial PORT-VaR Analysis
No full textThe continuous probability distributions can be successfully utilized to characterize and evaluate the risk exposure in applied actuarial analysis. Actuaries often prefer to convey the level of exposure to a certain hazard using merely a numerical value, or at the very least, a small number of numbers. In this paper, a new applied probability model was presented and used to model six different sets of data. About estimating the risks that insurance companies are exposed to and the revenues of the reinsurance process, we have analyzed and studied data on insurance claims and data on reinsurance revenues as an actuarial example. These actuarial risk exposure functions, sometimes referred to as main risk actuarial indicators, are unquestionably a result of a particular model that can be explained. Five crucial actuarial indicators are used in this study to identify the risk exposure in insurance claims and reinsurance revenues. The parameters are estimated using techniques like the maximum product spacing, maximum-likelihood, and least square estimation. Monte Carlo simulation research is conducted under a specific set of conditions and controls. Additionally, five actuarial risk indicators including the value-at-risk, tail-variance, tail value-at-risk, tail mean-variance, and mean of the excess loss function, were utilized to explain the risk exposure in the context of data on insurance claims and reinsurance revenue. The peak over a random threshold value-at-risk (PORT-VaR) approach and value-at-risk estimate are taken into account and contrasted for detecting the extreme financial insurance peaks
A New Bivariate Exponentiated Family of Distributions: Properties and Applications
No full textThe bivariate distributions are useful for the joint modeling of two random variables. In this paper, we have presented a bivariate version of the exponentiated family of distributions. Some desirable properties of the proposed bivariate family of distributions have been explored. These include the conditional distributions, the joint and conditional moments, dependence measures, reliability analysis, and maximum likelihood estimation of the parameters. A specific member of the proposed family has been explored for the power function baseline distribution giving rise to the bivariate exponentiated power function distribution. Some properties of the derived bivariate exponentiated power function distribution have been explored. The derived bivariate exponentiated power function distribution is fitted on some real data sets to see its suitability. It is found that the derived bivariate exponentiated power function distribution performs better than the competing distributions for modeling of the used data
Psychological Impact of COVID-19 on Families of Children with ASD and Typically Developing Children: A Case Study of Pakistan
No full textChildren with Autism Spectrum Disorder (ASD) and their parents, being a vulnerable population, were expected to be highly affected by the pandemic and its containment response. This study aims to analyze and compare the impact of COVID-19 on behavioral and mental well-being of ASD and TD (typically developing) individuals and their parents/caregivers in Pakistan. A total of 51 primary data samples from both groups were collected from Rawalpindi and Islamabad using a comprehensively designed survey, consisting of 6 sections related to participants and children demographics, parental exposure to COVID-19, impact of COVID-19 lockdowns, behavioral problems and ASD support during lockdown, parental distress (estimated via DASS21) and 2 open response questions. The study found that ASD families reported increased difficulties and required more commitment than before in nearly all aspects of life as compared to the TD group. Additionally, ASD children showed more behavioral problems in terms of aggressive, repetitive, and transition activities during lockdowns than before. Moreover, comparison of machine learning models ranked 5 significant factors contributing in parental distress which include family income, severity of ASD symptoms, type of ASD therapy, parental exposure to COVID-19, and impact of lockdowns on daily routines. Majority of participants reported the need for financial support, awareness, and proper planning from the government during the pandemic. The findings of this study provide evidence which highlights the necessity of collaborative interventions from both healthcare professionals and government authorities aimed at assisting parents in reducing distress and developing effective coping strategies, especially for individuals with ASD
Consistency Issues in Skew Random Fields: Investigating Proposed Alternatives and Identifying Persisting Problems
No full textMultiple researchers have proposed skew random fields derived from multivariate skew distributions, yet the consistency of these fields has been questioned. Mahmoudian (2018) and Saber et al. (2018) have put forth alternative suggestions to address these concerns. In our study, we identify that the random fields outlined by Mahmoudian (2018) continue to demonstrate consistency issues, suggesting a flaw in their definition. Finally we propose a skew random field and apply it to spatial prediction
New highly efficient one and two-stage ranked set sampling variations
No full textIn this paper, we proposed highly efficient ranked set sampling schemes to estimate the population mean. First, we proposed a new single-stage sampling scheme which we called new neoteric ranked set sampling. Second, we proposed a two-stage methods based on the systematic ranked set sampling and the new neoteric ranked set sampling. The performance of the proposed methods is compared with that of competitive two-stage methods through a Monte Carlo simulation study using various popular symmetric and asymmetric statistical distributions. The results show that the newly proposed methods are more efficient in estimating the population mean than the existing methods. The proposed methods are illustrated on data of the diameter and height of pine trees
Hybrid Approach Based on the CHAID Algorithm for Improving Classification Performance of Diabetes Data
No full textDiabetes, a chronic disease that is becoming more prevalent, presents increasing challenges, especially in low- and middle-income countries, where it is a growing burden. Egypt is the 9th most prevalent country for diabetes in the world, with estimated diabetes prevalence among adults at 15.2%, which raises urgent implications for early detection to limit complications including retinopathy, renal impairment and limb amputation. This study proposes a method to address classification of Type 2 diabetes (T2DM) through implementing and exploring the application of five machine learning algorithms: support vector machine (SVM), naïve Bayes (NB), K-Nearest Neighbor (KNN), Bayesian network (BNC) and stochastic gradient descent (SGD), along with CHAID algorithm to produce conditional segmentation variable to model non-linear interactions while improving expressivity of features used. CHAID analyses found that the best predictor of T2DM involved high levels of the hemoglobin A1c, and insulin resistance. The next best predictors were triglycerides and then followed by age, obesity, and blood pressure. Effects from the metabolic, cardiovascular, and lifestyle variables were small-to-moderate showing a significant amount of clustering. The hybrid model was developed as protection against overfitting, thus allowing robust and generalizable classification performance. The proposed hybrid models outperformed that of a single model. Specifically, SVM via CHAID and SGD via CHAID were able to obtain a perfect classification accuracy of 100% revealing the model's potential as a powerful tool for early detection and examination of risk of diabetes
A Novel Generated G Family for Risk Analysis and Assessment under Different Non-Bayesian Methods: Properties, Characterizations and Applications to USA House Prices and UK Insurance Claims Data
No full textThis study proposes a new and versatile family of continuous probability models known as the log-exponential generated (LEG) distributions, with particular emphasis on the log-exponential generated Weibull (LEGW) model as its prominent representative. By introducing an additional layer of parameterization, the family offers improved adaptability in shaping distributional forms, especially regarding skewness and heavy-tailed behavior. The LEGW formulation proves especially relevant for reliability data and for capturing rare but impactful events where asymmetry plays a major role. The work details the theoretical framework of the family through explicit expressions for its cumulative distribution function (CDF) and probability density function (PDF), alongside the corresponding hazard rate function (HRF). Several analytical characteristics are also investigated, including series representations and behavior in the extreme tail. To demonstrate practical value, the paper conducts risk evaluations employing sophisticated key risk indicators (KRIs) such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), and tail mean-variance measure (TMVq) across multiple quantile levels. Parameter estimation is addressed using several techniques, including maximum likelihood estimation (MLE), the Cramér–von Mises approach (CVM), and the Anderson–Darling estimator (ADE), in addition to their right-tail adjusted (RTADE) and left-tail adjusted variants (LTADE) to better capture extreme behaviors. Comparative performance analyses are carried out using both controlled simulation scenarios and real data from the insurance and housing sectors to test robustness under heavy-tail conditions. The findings highlight the effectiveness of the LEGW model in applied risk assessment, supported by evidence from insurance claims and economic datasets