Prediction of future failures in the log-logistic distribution based on hybrid censored data

We consider the prediction of future observations from the log-logistic distribution. The data is assumed hybrid right censored with possible left censoring. Different point predictors were derived. Specifically, we obtained the best unbiased, the conditional median, and the maximum likelihood predictors. Prediction intervals were derived using suitable pivotal quantities and intervals based on the highest density. We conducted a simulation study to compare the point and interval predictors. It is found that the point predictor BUP and the prediction interval HDI have the best overall performance. An illustrative example based on real data is given.

A complexity task of optimization in logistic distribution: A new approach to the green multi-objective vehicle routing problem

Logistic distribution involves many costs for organizations. Therefore, opportunities for optimization in this respect are always welcome. The purpose of this work is to present a methodology to provide a solution to a complexity task of optimization in Multi-objective Optimization for Green Vehicle Routing Problem (MOOGVRP). The methodology, illustrated using a case study (employee transport problem) and instances from the literature, was divided into three stages: Stage 1, “data treatment”, where the asymmetry of the routes to be formed and other particular features were addressed; Stage 2, “metaheuristic approaches” (hybrid or non-hybrid), used comparatively, more specifically: NSGA-II (Non-dominated Sorting Genetic Algorithm II), MOPSO (Multi-Objective Particle Swarm Optimization), which were compared with the new approaches proposed by the authors, CWNSGA-II (Clarke and Wright’s Savings with the Non-dominated Sorting Genetic Algorithm II) and CWTSNSGA-II (Clarke and Wright’s Savings, Tabu Search and Non-dominated Sorting Genetic Algorithm II); and, finally, Stage 3, “analysis of the results”, with a comparison of the algorithms. Using the same parameters as the current solution, an optimization of 5.2% was achieved for Objective Function 1 (OF{\displaystyle _{1}}; minimization of CO{\displaystyle _{2}} emissions) and 11.4% with regard to Objective Function 2 (OF{\displaystyle _{2}}; minimization of the difference in demand), with the proposed CWNSGA-II algorithm showing superiority over the others for the approached problem. Furthermore, a complementary scenario was tested, meeting the constraints required by the company concerning time limitation. For the instances from the literature, the CWNSGA-II and CWTSNSGA-II algorithms achieved superior results.

Lognormal and log-logistic distribution mixture analysis and application

In this paper, we analyze a mixture of Lognormal and Log-Logistic distribution. We estimate the parameters of the introduced distribution by using the expectation-maximization (EM) algorithm. Various phenomena in the field of medicine and economy could be modeled by this mixture. In this paper, it is used to construct new mortality model for determining the unisex premium rates in life insurance. The application of the model is illustrated in the case of Serbian population and its advantages are presented in the context of life insurance premium calculation.

Trends and country-level variation in age at first sex in sub-Saharan Africa among birth cohorts entering adulthood between 1985 and 2020

Background: Debuting sexual intercourse is a life course event marking exposure to pregnancy or fatherhood, and sexually transmitted infections (STIs), including HIV. We systematically analysed the timing, distribution, and trends in age at first sex (AFS) in 42 sub-Saharan Africa (SSA) countries. Methods: We collated individual-level AFS data from nationally representative household surveys across SSA. We used a log-skew-logistic distribution to model the distribution of AFS in a Bayesian spatio-temporal hierarchical random-effect model to estimate national trends of AFS over time and space, adjusting for age at report biases. Findings: Small changes in AFS are observed between the birth cohorts entering adulthood between 1985 and 2020, ranging 0.79 years [-0.01-1.51] and 0.48 [-0.03-1.92] for female and male, respectively. Northern SSA countries show appreciable increase in AFS but its gender gap remains the widest compared with minimal gender gap in the southern countries. The gender gap shows little evidence of change over time in most of the countries. Female's AFS approach to a similar age across SSA while male's AFS varies between regions. Proportion ever had sex under fifteen and eighteen are as high 34% and 83%, respectively. AFS distribution is typically asymmetric with most of sexual debut events occur in a span of 3.9 [3.4-5.0] years. Female teen often reports higher AFS compare to their late twenties while male teen report lower AFS; both sexes tend to recall a higher AFS in older ages compared to their thirties. Interpretation: Women debut sexually earlier and in a shorter span of age than men. Northern and southern SSA gender gap are distinctively different. Since the ratifying of HIV/AIDS intervention programs in SSA, a stagnant trend in AFS had remained in the countries most affected by the epidemic.

Hybrid Metaheuristic-Based Spatial Modeling and Analysis of Logistics Distribution Center

The location analysis of logistics distribution centers is one of the most critical issues in large-scale supply chains. While a number of algorithms and applications have been provided for this end, comparatively fewer investigations have been made into the integration of geographical information. This study proposes logistic distribution center location analysis that considers current geographic and embedded information gathered from a geographic information system (GIS). After reviewing the GIS, the decision variables and parameters are estimated using spatial analysis. These variables and parameters are utilized during mathematical problem-based analysis stage. While a number of existing algorithms have been proposed, this study applies a hybrid metaheuristic algorithm integrating particle swarm optimization (PSO) and genetic algorithm (GA). Using the proposed method, a more realistic mathematical model is established and solved for accurate analysis of logistics performance. To demonstrate the effectiveness of the proposed method, Korea Post distribution centers were considered in South Korea. Through tests with several real-world scenarios, it is proven experimentally that the proposed solution is more effective than existing PSO variations.

Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

A model for reconstructing trends and distribution in age at first sex from multiple household surveys with reporting biases

Age at first sex (AFS) is a key indicator for monitoring sexual behaviour risk for HIV and sexually transmitted diseases. Reporting of AFS data, however, suffer social-desirability and recall biases which obscure AFS trends and inferences constructed from it. We illustrated examples of the biases using data from multiple nationally-representative Demographic and Health Surveys household surveys conducted between 1992 and 2019 in Ethiopia (4 surveys), Guinea (4 surveys), Senegal (8 surveys), and Zambia (8 surveys). Based on this, we proposed a time-to-event, interval censored model for the AFS that uses overlapping reports by the same birth cohort in successive surveys to adjust reporting biases. The three-parameter log-skew-logistic distribution described the asymmetric and nonmonotonic hazard exhibited by empirical AFS data. In cross-validation analysis, incorporating a term for AFS reporting bias as a function of age improved model predictions for the trend of AFS over birth cohorts. The interquartile range for the AFS was 16 years to 23 years for Ethiopian and Senegalese women and 15 years to 20 years for Guinean and Zambian men. Median AFS increased by around one to 1.5 years between the 1960 and 1989 birth cohorts for all four datasets. Younger male respondents tended to report a younger AFS while female respondents tended to report an older AFS than when asked in later surveys. Above age 30, both male and female respondents tended to report older AFS compared to when surveyed in their late twenties. Simulations validated that the model recovers the trend in AFS over birth cohorts in the presence of reporting biases. At least three surveys are needed to obtain reliable trend estimate for a 20-years trend. Mis-specified reference age at which reporting is assumed unbiased did not affect the trend estimate but resulted in biased estimates for the median AFS in the most recent birth cohorts.

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

Modelling the COVID-19 Mortality Rate with a New Versatile Modification of the Log-Logistic Distribution

The goal of this paper is to develop an optimal statistical model to analyze COVID-19 data in order to model and analyze the COVID-19 mortality rates in Somalia. Combining the log-logistic distribution and the tangent function yields the flexible extension log-logistic tangent (LLT) distribution, a new two-parameter distribution. This new distribution has a number of excellent statistical and mathematical properties, including a simple failure rate function, reliability function, and cumulative distribution function. Maximum likelihood estimation (MLE) is used to estimate the unknown parameters of the proposed distribution. A numerical and visual result of the Monte Carlo simulation is obtained to evaluate the use of the MLE method. In addition, the LLT model is compared to the well-known two-parameter, three-parameter, and four-parameter competitors. Gompertz, log-logistic, kappa, exponentiated log-logistic, Marshall–Olkin log-logistic, Kumaraswamy log-logistic, and beta log-logistic are among the competing models. Different goodness-of-fit measures are used to determine whether the LLT distribution is more useful than the competing models in COVID-19 data of mortality rate analysis.