Thailand Statistician

The Zero-Truncated Poisson Generalized Lindley Distribution: Regression Model and Applications

Sat, 27 Dec 2025 00:00:00 +0700

This article introduces a new discrete distribution for nonzero count data. Some distributional properties, such as shape, probability generating function, moment generating function, and raw moments, are studied. The maximum likelihood method is applied to estimate the distribution parameters. A nonzero count regression model based on the proposed distribution is developed. The
performance of the proposed distribution and its regression model are shown through real nonzero count data, which shows that they outperform other competitive models. Therefore, the proposed model can be considered for count data excluding zero.

Interval Estimation in Location-Scale Family, Using Information Measures

Saeid Maadani, Gholam Reza Mohtashami Borzadaran, Abdolhamid Rezaei Roknabadi — Sat, 27 Dec 2025 00:00:00 +0700

Interval estimation is one of the important concepts in statistics. There are different methods to find a confidence interval for distribution parameters, but finding an optimal confidence interval is always a concern. On the other hand, it is important to find a confidence interval for the Shannon information of the ith order statistic when the distribution parameters are unknown. In the present paper, using information measures, we introduce an asymptotic confidence interval for scale parameter and the Shannon information of the ith order statistic related to the location-scale family. Via simulation study, we study the coverage probability and length of confidence intervals. Finally, some examples for hypothesis testing related to the Shannon information of the ith order statistic and the scale parameter are provided.

Application of Half Normal Distribution in Hybrid Group Adoption Sampling Plan for Life Tests

B. Srinivasa Rao, J. Siva Ram Prasad, B. Vara Prasad Rao, M. Sudhakar — Sat, 27 Dec 2025 00:00:00 +0700

This article deals with the discussion of a hybrid group adoption sampling plan depending upon truncated lifetimes of an object whose lifetime accompanies half normal distribution. By considering a size of a group of objects, the least quantity of testers and the value of acceptance number needed are calculated for identified customer’s risk and closing time of the test. The numeric value of the operating characteristic function to different standard levels are evaluated, also minimum ratios for real mean life period to an identified life period for specified producer’s risk are acquired. Obtained outputs are elucidated with some illustrations.

Modeling Heavy-Tailed Data via the New Topp-Leone Heavy-Tailed Gompertz-G Family of Distributions

Sat, 27 Dec 2025 00:00:00 +0700

In this article, we introduce a new distribution named, Topp-Leone Heavy-Tailed GompertzG (TL-HT-Gom-G) family of distributions. Several mathematical and statistical properties of the new TL-HT-Gom-G family of distributions including quantile function, moments, moment generating function, Renyi entropy, distribution of order statistics, stochastic orderings are derived. Risk ´measures and a numerical simulation study are also presented for this family of distributions. To estimate the model parameters, we use six different estimation methods, namely, maximum likelihood, Anderson-Darling, Right-Tail Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, and Cramer-von Mises. A simulation study is further performed to assess these estimation techniques ´and finally we demonstrate the applicability of the new family of distributions using applications to three real data sets.

Order Statistics from Inverse Lomax Log-Logistic (IL-LL) Distribution

Zakir Ali, Zaki Anwar, Iftkhar Khan — Sat, 27 Dec 2025 00:00:00 +0700

Random variables with order have found extensive use across various fields, including sports, seismology, reliability, quality control, actuarial science, and more. This study focuses on the inverse Lomax log-logistic distribution. Inverse Lomax log-logistic distribution is a flexible and robust model that exhibits several noteworthy statistical properties. Its probability density function is typically right-skewed and decreasing, making it suitable for modeling positively skewed data. We establish precise formulations for moments, providing valuable tools for determining diverse statistical properties of this distribution. We compute moments at various parameter values to enhance our understanding of the distribution. Further, these moments are used to determine the best linear unbiased estimators.

A New Exponent-Generator Family of Statistical Distribution with Simulation and Analysis to Cancer Data

Nuzhat Ahad, Ahmad SP SP, Reshi JA — Sat, 27 Dec 2025 00:00:00 +0700

A novel family of distribution has been introduced, named as "exponent-Generator family of statistical distribution", designed for optimal univariate modeling. We explored the structural and characterizing properties of a newly proposed distribution, the exponent power function (EPF) distribution. We provide explicit expressions for the probability density function (PDF), cumulative distribution function (CDF), reliability function (RF), and hazard rate function (HRF). Also the r-th moment, moment generating function (MGF), and the order statistics are obtained. The manuscript also includes a detailed discussion on the shapes of PDF and HRF for selected parameter values, providing valuable insights into the behavior of distribution. Moreover, we discussed maximum likelihood estimation (MLE) and Bayesian estimation method. The adaptability of the proposed distribution is evaluated by analyzing the three real data sets related to lifetime of cancer patients as well as a simulated dataset.

A New Class of Models with Bathtub Shaped Hazard Rate Functions

Regent Retrospect Musekwa, Boikanyo Makubate — Sat, 27 Dec 2025 00:00:00 +0700

In the present research, we compound the alpha power transformation distribution with the power
series distribution to create a novel distribution known as the alpha power transformed-G Power Series (APT-GPS) distribution. The APT-GPS distribution’s statistical characteristics are discovered. The density and hazard rate life plots are shown in a range of forms using a Weibull baseline distribution. Additionally, a simulation study is carried out to evaluate the effectiveness of the maximum likelihood estimates. Lastly, some samples of bladder cancer data and United Kingdom (UK) Covid-19 data are evaluated for illustrative purposes. The results show that, in comparison to other non-nested distributions taken into consideration in this article, the proposed distribution offers a better fit as it exhibits the lowest goodness of fit statistics values and the highest accuracy rate on both data sets.

Parameter Estimation in Case of Incomplete Frames using Ratio Estimators

Shilpa Yadav, Pankaj Nagar — Sat, 27 Dec 2025 00:00:00 +0700

Existence of a well defined and perfect sampling frame is the fundamental requirement of any
sample survey. But there is enough evidence to support the fact that a perfect sampling frame that
captures all the individual units of the population is rarely available, especially for a dynamic population where a constant movement of the units of the population is observed. In such cases, the sample
collected can not be considered as a good representative of the population and the problem of incomplete frame arises. The results so drawn can immensely change the survey results and influence the legitimacy of the research. This study deals with the incomplete frame problem using ratio method of estimation, where the information on the auxiliary or ancillary variable is collected in the first phase and a second phase sample is then drawn to obtain estimates of the population mean of the characteristic under study and its mean square error up to first order approximation. Two different estimators, viz., combined ratio estimator and separate ratio estimators have been used and their efficiencies are compared. Further, the results are illustrated numerically with the help of Monte-Carlo simulations.

Estimation of P(X < Y ) for Morgenstern Type Bivariate Exponential Distribution Based on Ranked Set Sample

Shiny Mathew, Manoj Chacko — Sat, 27 Dec 2025 00:00:00 +0700

Estimation of R = P(X < Y ) has been intensively investigated in the literature using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimation of R when X and Y are dependent random variables based on ranked set sample (RSS). The maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of R are obtained based on RSS when (X, Y ) follows Morgenstern type bivariate exponential distribution. BEs are obtained based on both symmetric and asymmetric loss functions. The percentile bootstrap and HPD confidence intervals for R are also obtained. Simulation studies are carried out to find the accuracy of the proposed estimators. A real data is also used to illustrate the inferential procedures developed in this paper.

On Zero-Inflated Poisson Garima Distribution and its Applications to Count Data

Peer Bilal Ahmad, Zehra Skinder — Sat, 27 Dec 2025 00:00:00 +0700

Excessive zero counts are one of the causes of over-dispersion in count data that is often observed in different fields. In this paper, we propose a new zero-inflated model namely ‘the zero-inflated Poisson Garima distribution’ to handle excessive zero counts. Various structural properties including reliability characteristics, generating functions, moments, etc. are obtained. Also, the parametric estimation of the proposed model is obtained using maximum likelihood method of estimation. Furthermore, a simulation study is carried out to check the behaviour of maximum likelihood estimators. Moreover, the proposed model and the baseline model are distinguished using two different test procedures. Finally, two real-life data sets taken from different domains are considered to validate the empirical applications of the proposed model.

Optimizing Smart Pole Placement: A Strategic Set Covering Approach in Phra Nakhon Si Ayutthaya

Sat, 27 Dec 2025 00:00:00 +0700

This research introduces a method for optimally placing smart poles in urban areas, using a model based on a set covering problem principles and hexagonal space partitioning, solved with QGIS and IBM CPLEX. Applied to the Phra Nakhon Si Ayutthaya District, it identified 668 optimal spots for smart poles. The results emphasize the significance of proper location selection for smart pole functionality and its potential application in other cities. This optimization can increase urban efficiency and citizens quality of life.

An ARL Derivation Based on Explicit Formulas to Detect Shifts in the Mean of Seasonal Time-Series Models Running on a CUSUM Control Chart

Wilasinee Peerajit — Sat, 27 Dec 2025 00:00:00 +0700

Herein, we propose a derivation of the average run length (ARL) to detect shifts in the mean of seasonal time-series models running on a CUSUM control chart based on explicit formulas by solving the Fredholm integral equation of the second kind. The existence and uniqueness of the solution were guaranteed by applying Banach’s fixed-point theorem. We applied the explicit formulas for the ARL to detect changes in the mean of a long-memory SARFIMA process with exponential white noise running on a one-sided CUSUM control chart. When comparing the performance of the proposed method with the ARL obtained via the standard numerical integral equation (NIE) method, the former performed better for small-to-moderate shifts in the process mean under the same conditions and circumstances. Moreover, its percentage accuracy (a benchmark for the ARL) was greater than 95%, thereby indicating excellent agreement between the two methods. In addition, the computer processing time for the proposed method was considerably faster than that required for the NIE method. Hence, this explicit formulas approach provides a novel means of determining the ARL for detecting changes in the mean of a long-memory SARFIMA process with exponential white noise running on a one-sided CUSUM control chart. Finally, the proposed and NIE methods were applied to applications with real-life data to determine their efficacy.

An Efficiency of DMEWMA Control Chart to Monitor Changes in Process Mean on First Order Moving Average Model with Application to Daily Natural Gas Data

Julalak Neammai, Yupaporn Areepong Areepong, Saowanit Sukparungsee — Sat, 27 Dec 2025 00:00:00 +0700

The double modified exponentially weighted moving average (DMEWMA) control chart is a mixture of two modified exponentially weighted moving average (MEWMA) control chart for monitoring shifts in the process mean. The average run length (ARL) is important for evaluating the performance of control charts. The purpose of this research is to derive the exact formula for ARL on the DMEWMA Control Chart for moving average process order one in one-sided. The absolute percentage relative error (APRE) was used to compare the accuracy of the exact formula to four quadrature distinct numerical integral equation approaches (NIE). Following that, Banach's fixed point theorem is applied to ensure its existence and uniqueness. Furthermore, the effectiveness of the DMEWMA control chart is compared to that of the EWMA and MEWMA control charts. The ARL, the Standard Deviation Run Length (SDRL), and the relative mean index (RMI) are measurement tools used to assess a control chart's capacity to detect process mean. The results demonstrate that the ARL generated by the exact formula and the NIE approach are almost the same, but the exact formula can assist reduce computational (CPU) time. This is further expanded to provide performance comparisons with the EWMA and MEWMA control charts. For almost all scenarios, the DMEWMA control chart outperforms the EWMA control chart and the MEWMA control chart. Finally, the ARL analytical solution gets utilized on real-world data.

A Flexible Form for the Topp-Leone Distribution: Properties and Different Methods of Estimation

Hiba Z. Muhammed, El-Sayed A. El-Sherpieny, Amira Hassan EL-Sayed — Sat, 27 Dec 2025 00:00:00 +0700

It is important to find new simple explicit forms for distributions instead of their old implicit forms which cause some problems in mathematical properties and generating random numbers. In this paper, a simple transformation is applied to the Topp-Leone distribution giving a new distribution called the flexible Toppe-Leone distribution having more flexibility in mathematical properties and simulation studies specially generating random numbers. Some different methods of estimation are used for the flexible Toppe-Leone distribution via classical and Bayesian approaches using a progressive Type-II censoring scheme, a simulation study is performed to compare estimators' behaviors of the estimation methods.

A Systematic Review and Meta-analysis of Dane Fukang Decoction and Gestrinone for Treatment of Endometriosis

Sat, 27 Dec 2025 00:00:00 +0700

Endometriosis is a chronic gynecological condition influenced by hormones that frequently causes severe pelvic pain and other concerning symptoms such as heavy or irregular menstrual bleeding, painful intercourse, fatigue, nausea, and infertility. While surgery is often required, the rates of recurrence after surgery remain high. Objective. This systematic review and meta-analysis aimed to determine the efficacy of Dane Fukang decoction and Gestrinone for treating endometriosis after surgery. A literature search was conducted in the primary electronic databases, with studies published from inception until January 2024. The analysis included in randomized controlled trials (RCTs) that compared Dane Fukang decoction to Gestrinone for endometriosis treatment after surgery. Meta-analyses were conducted using random-effects models, calculating pooled odds ratios (OR) and 95% confidence intervals (CI). A total of six RCTs involving 658 patients were included. The meta-analysis showed that Dane Fukang decoction significantly improved effectiveness compared to gestrinone treatments. The random effect model analysis yielded an odds ratio of 2.72 (95% CI: 1.13 to 6.54, p=0.05) with an I2 value of 56%, suggesting moderate heterogeneity among the included studies. No serious adverse events were reported with either intervention. This systematic review and meta-analysis provide evidence supporting the superior efficacy of Dane Fukang decoction over gestrinone as a post-operative treatment for endometriosis to improve overall clinical outcomes.