This research explores Bayesian and classical estimation methods for the Log Logistic distribution, focusing on upper record values in bladder cancer remission times. Bayesian estimates are derived under informative and non-informative priors, using independent Gamma distributions to model the shape and scale parameters. Due to the non-closed form of Bayes and Maximum Likelihood estimators, numerical techniques such as Newton–Raphson and Markov Chain Monte Carlo simulations are utilized for their computation. Sensitivity analysis, involving variations in hyperparameters, evaluates the impact of prior information on estimation outcomes. The study includes a simulation study and an analysis of real-world data from bladder cancer remission times to assess the efficacy of these numerical methods. This research contributes to advancing the understanding of statistical methods for analyzing upper record values in medical research contexts, particularly in modeling and interpreting remission times for bladder cancer patients.

This study introduces a novel statistical family known as the Ristić-Balakrishnan-Heavy-Tailed-Type II Topp-Leone-G (RB-HT-TIITL-G). The research explores key statistical properties, including hazard rate function, quantile function, moments, stochastic ordering, and order statistics. Furthermore, essential risk measures such as value at risk, tail variance, and tail variance premium are derived. Several parameter estimation methods, including maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramér-von Mises, and Anderson-Darling estimators, are applied. Monte Carlo simulations evaluate the consistency of these estimation techniques. Lastly, the model’s effectiveness is validated using real-world data, demonstrating its suitability for modeling diverse data sets.

This study aims to elucidate the critical relationship between temperature variations and power outages. We propose to employ the Weibull distribution, a fundamental tool in reliability analysis, to assess the impact of temperature on power grid failures using the SigmaXL statistical tool. This research adopts a two-parameter Weibull distribution and we set our alpha () value as 0.05 with maximum likelihood as the method of estimation. The research utilized a historic multi-sourced comprehensive data on electricity demand, temperature, and power outages of a complete year. We utilised Mean-Time-To-Failure as a crucial metric in reliability analysis, representing the average lifespan of a given asset or component, such as the power grid network. The estimated Weibull shape parameter (β = 3.662) was greater than 1. This suggests a “failure rate” (outage likelihood) that increases over time, potentially influenced by temperature. The estimated scale parameter (η = 32.614 days) translates to a mean time to failure (MTTF) of 29.416 days. This indicates that on average, power outages are expected to occur every 29.42 days, considering the temperature data. Finally, we found that time is directly proportional to cumulative failure probability in predicting power outage possibilities.

Tourist arrivals play a vital role in the broader tourism ecosystem, substantially contributing to the economy. The global landscape has witnessed significant growth in international arrivals over the years, and Nepal has not been an exception to this trend, experiencing a steady influx of inbound tourists. Although tourist numbers are increasing, the lack of research in forecasting future arrivals is evident, highlighting the pressing need for comprehensive forecasting mechanisms to efficiently manage tourism resources and sustainably accommodate the growing influx of visitors. In order to gain insights into the dynamics of international tourist arrivals in Nepal, we conducted a comparative analysis using two distinct forecasting techniques: Seasonal Autoregressive Integrated Moving Average (SARIMA) and the Exponential Smoothing technique. Our analysis spanned from January 1992 to December 2023, enabling us to formulate forecasts for the upcoming months up to December 2030. The findings of our study underscore the suitability of all three models—namely, SARIMA, Winter Additive, and Winter Multiplicative—as effective tools for projecting international arrivals in Nepal. However, upon careful examination, the Winter Multiplicative model emerged as the most appropriate model for forecasting Nepal's international arrivals. This model aligned strongly with the observed data, enhancing its predictive accuracy. The implications of our research are far-reaching, offering valuable insights for various stakeholders within Nepal's tourism industry. These insights can guide tourism planners, policymakers, and other relevant entities in formulating well-informed strategies to strengthen and sustain the growth of the tourism sector in Nepal. As the nation continues to position itself on the global tourism map, equipped with data-driven forecasts, we believe that our study provides an essential resource for shaping the trajectory of Nepal's tourism industry in a positive direction.

Abstract Haematocrit Levels is defined as the proportion, by volume, of the blood that consists of red blood cells. This study was conducted to model the progress of haematocrit levels over time in kidney patients after their transplant and to determine how the progress depends on the age and gender of the patient and other factors. This is a longitudinal study, and haematocrit level was considered as a response while the covariates were time, gender, age, cardio-vascular problem during the years preceding the transplantation, and rejection symptoms during the first three months after the transplantation took place of the patients. Different statistical methods such as, multivariate regression model, two stage analysis and linear mixed effects model were employed to explore the progress of haematocrit over time. Models revealed that haematocrit levels in kidney transplant patients evolve over time. Gender and Age of the patient have significant effect on the evolution of haematocrit levels. Males tend to have a high increase in haematocrit levels over time than females. With regards to age, haematocrit levels tend to increase with increasing age. Moreover, it was observed that experience of cardio-vascular problems before trandplant and rejection symptoms did not have a significant effect on the progress of haematicrit levels. The growth of Haematocrit levels evolve over time follows a quartic time effect. Change in haematocrit levels varies according to gender and age of the patient. Patients starting with low haematocrit levels tend to have a larger increase over time.

Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution’s parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions.

The goal of this research is to create a new general family of Topp-Leone distributions called the Topp-Leone Cauchy Family (TLC), which is exceedingly versatile and results from a careful merging of the Topp-Leone and Cauchy distribution families. Some of the new family’s theoretical properties are investigated using specific results on stochastic functions, quantile functions and associated measures, generic moments, probability weighted moments, and Shannon entropy. A parametric statistical model is built from a specific member of the family. The maximum likelihood technique is used to estimate the model’s unknown parameters. Furthermore, to emphasize the new family’s practical potential, we applied our model to two real-world data sets and compared it to existing rival models.

This paper presents some efficient classes of estimators of population mean on current occasion in the presence of random non-response under a two-phase successive sampling set-up. The suggested classes of estimators are proposed for simple random sampling under various situations of non-response. The properties of proposed estimators have been discussed up to first order of approximation. The efficiency of the presented estimators has been contrasted with the estimators for the complete response scenarios. Two real and two artificially generated data sets are used. The efficacy of the proposed classes of estimators over the existing estimators is checked theoretically and empirically. The numerical comparison supports the proposed estimators.

The present paper deals with the problem of estimation of finite population mean of study variable using two auxiliary variables in two-phase sampling scheme using predictive approach in case of missing values of the study variable and unknown population mean of first auxiliary variable. Four classes of such estimators have been proposed using this predictive approach. The expressions of bias and mean square errors are derived up to first order of approximation. The optimal values of the constants involved in the proposed classes of estimators have been obtained and thus minimum mean square errors of the proposed classes are obtained in this study. The empirical and graphical comparisons with regression type estimators (under single phase and double phase sampling scheme) and also among themselves have been made for evaluating the performance of the proposed classes for different choices of non-responding units. Five real data sets and three simulated data sets following normal distribution have been used to evaluate the performance of the proposed classes. Numerical findings confirm the theoretical results obtained regarding superiority of proposed classes of estimators over the conventional regression type estimators in terms of percent relative efficiencies.