Thailand Statistician

A New and Generalized Class of Log-logistic Modified Weibull Power Series Distributions with Applications

Broderick Oluyede, Neo Dingalo, Fastel Chipepa — Sun, 31 Mar 2024 00:00:00 +0700

A new generalized class of distributions called the log-logistic modified Weibull power series (LLoGMWPS) distribution is developed and presented. The LLoGMWPS class of distributions generalizes several distributions including the log-logistic exponential power series, log-logistic Weibull power series, log-logistic Rayleigh power series, log-logistic power series class of distributions and
a host of other distributions including log-logistic modified Weibull, log-logistic Weibull, and loglogistic distributions. The special case of the log-logistic modified Weibull Poisson (LLoGMWP) and log-logistic modified Weibull Logarithmic (LLoGMWL) distributions are studied in detail. We apply the method of maximum likelihood to estimate the parameters of this new distribution. Finally,
real data examples are presented to illustrate the usefulness and applicability of both LLoGMWP and LLoGMWL distributions.

An Acceptance Sampling Plan for Testing of Product’s Life using New Weibull-Rayleigh Distribution

Muhammad Bilal , Muhammad Mohsin, Salman Abbas — Sun, 31 Mar 2024 00:00:00 +0700

Acceptance sampling plans are vital in account to make decision about the life of the product. In present article, we propose an acceptance sampling plan for the life length of a product which follows Weibull-Rayleigh distribution. Plans are designed for both finite and infinite sample sizes at different combinations of parameters. Operating characteristic curves are derived to demonstrate the
efficiency of the proposed acceptance sampling plan. Numerical and graphical presentation of the proposed plans lead us to draw a useful conclusion for the acceptance probability.

Exponentiated Approach on Intervened Exponential Model with Real-Life Study

Vilayat Ali Bhat, Sudesh Pundir — Sun, 31 Mar 2024 00:00:00 +0700

In this article, the exponentiated approach has been utilized to develop the new extension of Intervened Exponential distribution named as an exponentiated intervened exponential distribution. The
various statistical properties of the proposed distribution have been derived, whereas the reliability
characterization involves some special functions such as the reliability function, hazard rate, aging intensity, and the mean residual life function. In addition, the other major results presented in the article include order statistics, stress strength reliability, and stochastic ordering. Furthermore, the entropy measures that are Shannon and Renyi are also derived. The method of the maximum likelihood ´
approach has been used for parameter estimation. Monte Carlo simulation study is recommended followed by the acceptance-rejection algorithm for data generation and in this study, the behavior of the estimated parameters is discussed based on the calculated values of bias and the mean square error. Lastly, the real-life data set is analyzed to ensure the applicability of the newly developed model.

Comparison between the Two Haung-Kotz FGM Types by Fisher Information in Order Statistics and Their Concomitants

Haroon Mohamed Barakat, Elsaied Mahsoub Nigm, Afaf Hatem Syam — Sun, 31 Mar 2024 00:00:00 +0700

The Fisher information (FI) about the shape-parameter vectors of the two Huang-Kotz FGM types
is investigated. We study analytically and numerically the FI matrix (FIM) related to an order statistic
(OS) and its concomitant for each of these types. A comparison between the two types based on FI is
carried out.

A Simple Profile Likelihood-based Confidence Interval for the Risk Ratio in Rare Events Meta-analysis

Patarawan Sangnawakij — Sun, 31 Mar 2024 00:00:00 +0700

Meta-analysis refers to a quantitative method for performing statistical analysis and summarizing results from independent studies, to draw overall conclusions. When the small number of events in individual studies are observed in one or both treatment groups, the classical meta-analysis can lead to perversion because of data sparsity. In this paper, two confidence intervals for the risk ratio in
rare events meta-analysis are proposed. They are derived through the profile likelihood ratio method. An extensive simulation study is performed to evaluate the performance of the proposed estimators. These are compared to the Wald-type and Mantel-Haenzel confidence intervals. By mean of simulations, our confidence interval is found to have a good performance in general cases in the study. It is also robust; in other words, regardless of the number of studies, its simulated coverage probability is close to the specified confidence coefficient with an acceptable average length. Real data analysis on epidemiology and transmission is conducted to assess the computational feasibility of the proposed methods.

Confidence Intervals for Common Mean of Delta-Lognormal Distributions Based on Left-Censored Data with Application to Rainfall Data in Thailand

Warisa Thangjai, Sa-Aat Niwitpong — Sun, 31 Mar 2024 00:00:00 +0700

In environmental data analysis, it is common to encounter left-censored data, such as rainfall and particulate matter data, which follow the delta-lognormal distribution. This paper focuses on estimating confidence intervals for the common mean of delta-lognormal distributions based on left-censored data. The confidence intervals are constructed using four approaches: the generalized confidence interval approach, the Bayesian approach, the parametric bootstrap approach, and the adjusted method of variance estimates recovery approach. The performance of these approaches is evaluated through Monte Carlo simulations using RStudio programming. The results reveal that for the number of sample cases k = 3, the generalized confidence interval approach and the adjusted method of variance estimates recovery approach performed very well when the sample sizes were small, whereas the Bayesian approach performed exceptionally well for moderate and large sample sizes. For the number of sample cases k = 6, the generalized confidence interval approach and the adjusted method of variance estimates recovery approach performed very well for small and moderate sample sizes, while the Bayesian approach excelled for large sample sizes. The results are illustrated with rainfall data from three regions of Thailand.

Intercept-only Model under Non-normality

Bouchafaa Asma, Djeddour-Djaballah Khedidja, Benjrada Mohammed Essalih — Sun, 31 Mar 2024 00:00:00 +0700

In this paper, we consider a linear regression intercept-only model under the hypothesis of nonnormality. Generally, the errors are independent and normally distributed. In our case, we assume the errors are independent and follow an exponential law. We prove the consistency and establish the asymptotic distribution of the maximum likelihood estimator for the parameter of the interceptonly model. Numerical simulations confirm the accuracy of this estimator. We notably exhibit the advantages of the maximum likelihood estimator compared to the classical ordinary least square estimator. Finally, we applied the approach to a data of a real-life example, namely the Canadian lynx data.

Calibrated Estimator for Sensitive Variables under Stratified Random Sampling

Riffat Jabeen, Muhammad Kamran Aslam, Aamir Sanaullah, Azam Zaka — Sun, 31 Mar 2024 00:00:00 +0700

Calibration sampling is a general tool to adjust the sampling weights and enhance the precision of the estimates. This technique is also helpful to reduce the non-response errors. In order to remove or minimize the biases produced by non-response errors and variances, the calibration technique is utilized. In this paper, Calibration technique is used to reduce the distance between the calibrated weights and the given distance measure. We propose new calibration estimators for estimating the population of a sensitive variable based on scrambled responses collected using some improved random response device and auxiliary information. This study is to propose some improved calibrated generalized estimators for estimation of population mean of a quantitative sensitive variable. The results show that the proposed estimator having an extra calibration constraint is more efficient.

Improved Estimation of Population Mean in Simple Random Sampling Using Attribute

Shashi Bhushan, Anoop Kumar — Sun, 31 Mar 2024 00:00:00 +0700

This article discusses the problem of estimation of population mean using the information on an auxiliary attribute under simple random sampling. An improved class of estimator is suggested and the expression of the mean square error is determined up to the first order of approximation using Taylor series method. The usual mean estimator, classical ratio estimator envisaged by Naik and Gupta (1996) and Abd-Elfattah et al. (2010) estimators are identified as the members of the proposed class of estimator. The theoretical conditions are obtained by comparing the mean square error of the proposed estimators with the mean square error of the existing estimators under which the proposed class of estimator dominates the existing estimators suggested till date. A numerical study using real populations and a simulation study using artificially generated populations are conducted to enhance the theoretical findings.

Instant Exchange Analytics: A Compelling Mathematical Model for Real-Time Debt Instrument and Cash Conversion Rates

Sun, 31 Mar 2024 00:00:00 +0700

This research investigates a model for determining instantaneous debt instrument prices for converting debt securities into cash over time. The study employs three interest rate models: Vasicek, Cox-Ingersoll-Ross, and Hull-White, using historical daily treasury bill interest rates from January 2004 to October 2020. The findings suggest that the Hull-White model outperforms the Vasicek and Cox-Ingersoll-Ross models, simulating interest rates for determining debt-to-cash exchange rates. Additionally, a real-time continuous debt-to-cash conversion prototype is developed using zero-coupon government bonds with maturities of no more than 10 years, traded in the Thai secondary debt market as a case study.

Determining the ARL for a Shift in the Mean of a Long-Memory ARFIMA(1, d, 1)(1, D, 1)s Process with Exponential White Noise Running on a CUSUM Control Chart

Wilasinee Peerajit — Sun, 31 Mar 2024 00:00:00 +0700

The CUSUM control chart is a well-known statistical process monitoring tool that is sensitive to small-to-moderate shifts in a process parameter. Herein, we provide a solution for the average run length (ARL) for a shift in the mean of a long-memory process with exponential white noise running on a CUSUM control chart based on the analytical integral equation (AIE) approach. Its existence and uniqueness were proven by applying Banach's fixed-point theorem. The numerical integral equation (NIE) method was used to verify the accuracy of the proposed AIE approach by comparing the percentage accuracies for various out-of-control ARL situations. We also recorded their computational times. The results of using the AIE and NIE approaches are in close agreement (percentage accuracy > 95%) but the time required to compute the ARL using the former was significantly shorter. A major advantage of using the AIE approach was in finding the optimal values for reference value (k) and control limit (b) very quickly when the process is in-control. Moreover, their optimal values for the minimum out-of-control ARL for the mean of a long-memory process with exponential white noise running on a CUSUM control chart are also derived. An illustrative example with real data is given to illustrate the practicability of the proposed method. The practical scenario involves analysing natural gas futures prices using the AIE method on the CUSUM control chart in order to track changes in stock prices, which is the point in making profitable decisions for investors.

Applications to Physical Data Using Four-Parameter Inverted Topp-Leone Model

Amal Soliman Hassan, Ehab Mohamed Almetwally — Sun, 31 Mar 2024 00:00:00 +0700

The Kumaraswamy Marshall-Olkin inverted Topp-Leone (KMOITL) distribution is a new four-parameter generalized version of the inverted Topp-Leone (ITL) distribution proposed in this research. The Marshall-Olkin ITL distribution is a novel model, while the Kumaraswamy ITL and ITL distributions are existing sub-models in the proposed distribution. Different shapes of the density and hazard rate functions are provided by the KMOITL distribution, which has three shape parameters and one scale parameter. The KMOITL’s density function can be written as a linear combination of the inverted Topp-Leone density. We construct several statistical expressions for the proposed KMOITL model. The KMOITL distribution parameters are estimated using maximum likelihood and Bayesian estimation techniques. In light of symmetric and asymmetric loss functions, Bayesian estimators are explored. The performance of the suggested estimating techniques is evaluated using simulation results. Finally, the suggested model is tested based on physical real data, with the findings demonstrating the KMOITL distribution’s higher performance over some other models.

A New Exponential Ratio-Type Estimator of Population Mean Using Mean and Median with Two Auxiliary Variables under Double Sampling

Ronald Eleazer Kurbah, Phrangstone Khongji — Sun, 31 Mar 2024 00:00:00 +0700

Using auxiliary information for estimating the study variable is a popular and well established technique to enhance the efficiency of the estimator. In this paper, we have considered an exponential ratio-type estimator under double sampling scheme involving two auxiliary variables. Both cases of independence and dependence of auxiliary variables have been considered. Here, we make use of the sample mean and sample median of the auxiliary variables of both phases with the intention to improve upon the efficiency of the said estimator. It is found that the proposed estimator is more efficient than the regression estimator proposed by Vadlamudi et al. (2017) with one auxiliary variable and also over other classical estimators. The study was tested empirically using simulated data.

Stochastic Properties of Topp-Leone Generated Family of Distributions

Amit Kumar Misra, Ruby Chanchal, Vaishali Gupta — Sun, 31 Mar 2024 00:00:00 +0700

Topp-Leone generated family of distributions contains continuous distributions having bathtub shaped hazard rates. In this paper, we compare two random variables from this family of distributions using stochastic orderings. We also consider a special case of this family of distributions, namely, Topp-Leone exponential distribution and investigate few reliability indicators of this distribution such as hazard rate function, reversed hazard rate function, mean residual life function, and expected inactivity time. Renyi entropy measure for the Topp-Leone exponential distribution has also been discussed. Moreover, we define the Topp-Leone generated log-logistic distribution and the Topp-Leone generated Lomax distribution using the genesis of the Topp-Leone generated family of distributions. We also present real data applications to discuss the importance of this family of distributions.

Study of Merger and Acquisition (M&A) with Spline function in AR Time Series Model Under Bayesian Framework

Jitendra Kumar, Mohd Mudassir, Varun Agiwal — Sun, 31 Mar 2024 00:00:00 +0700

In this paper, we use an autoregressive model to investigate the behavior of mergers and acquisitions. It studies a non-linear time trend, which is approximately converted into a linear time trend using the spline function, which divides the series into piecewise linear segments between the knots. These knots are the change points where the trend pattern gets changed. The major aim of this study is to offer a merged autoregressive spline (M-ARS) model that can be used to analyze the influence of the merger on the parameters as well as model behavior. First, we obtained an estimation setup based on the well-known classical least square method and posterior distributions under the Bayesian approach with different loss functions. Then, the effect on the series based on the merger variable is significantly determined by the Bayes factor. The applicability of the proposed model is illustrated based on a simulation study and real application in the Indian banking sector.