This paper introduces a four-parameter extended odd log-logistic-Lindley distribution from which moments, hazard, and quantile functions are then obtained. The statistical properties of this distribution show the high flexibility of the proposed distribution. The maximum likelihood and least-squares estimators of the extended odd log-logistic-Lindley parameters are studied. Moreover, a simulation study is carried out for evaluating the performance of the estimation methods, and the usefulness of the new distribution is illustrated using two real data sets. Finally, Bayesian analysis and efficiency of Gibbs sampling are provided on the basis of two real data sets.

Mathematical risk modeling in a market economy has become a key tool for analyzing consumer behavior under conditions of unstable prices and shifting supply. In this study, we combine Paul Samuelson’s classical theory of revealed preferences with dynamic demand and supply mechanisms, using Afriat’s theorem and extensions by Varian and Mas-Colell to construct utility functions without survey data. Critical voices (e.g. Dryzek) prompt a reexamination of the assumptions of full information and fixed preferences, inspiring our proposal of the F(w, z) function that accounts for the strength of market fluctuations. Empirical simulations and an analysis of market equilibrium stability yield new insights for economic policy and marketing strategies.

In this paper, we develop a Bayesian nonparametric approach for analyzing weighted survival data. Specifically, we employ the Dirichlet Process Burr XII Mixture Model (DPBMM) to estimate the underlying density and survival functions when the observed data are weighted. Parameters are inferred using Markov chain Monte Carlo (MCMC) methods, and the Metropolis- Hastings algorithm is applied to obtain de-biased samples from the weighted observations. Numerical illustrations are provided using both simulated and real lifetime data, including the presence of censored observations. The performance of the proposed method is compared with classical kernel density estimates to demonstrate its flexibility in modeling complex and heavy-tailed distributions.

Modern local government units form important links in the socio-economic structure of the country and their development is closely related to the occurrence of degraded areas. This study focused on identifying the social, economic and environmental factors that determine the occurrence of degraded areas requiring revitalisation in Polish local government units. The article used unit data from a Statistics Poland survey based on the SG-01 report: Municipal Statistics – Revitalisation2. The PROFIT (PROperty FITting) multidimensional scaling program for local level territorial units was applied. The program takes into account the delimitation of rural areas based on the typology of Functional Urban Areas. The results were visualised through perception maps. Calculations and figures were made in Statistica 13. The focus on the problematic areas revealed the variety of challenges faced by local government units in their revitalisation activities. The survey was thus complemented by an analysis of the results of the undertaken revitalisation projects. The comprehensive analysis of the factors causing the degradation of areas in local government units and the effects of the revitalisation may prove important tools for rural and urban policy makers and planners in developing effective local development strategies and may have an impact on the quality of life of residents.

This study introduces and evaluates the truncated Schröter recursive algorithm for computing aggregate claim amounts in the insurance sector. The algorithm addresses the limitations in the existing methods by incorporating truncation at 1, which is crucial for an accurate modelling of insurance claims where the events leading to a claim are pivotal. Using the AutoCollision dataset, the study compares the truncated Schröter algorithm with the Panjer and Schröter recursion algorithms, focusing on computational efficiency and accuracy. Furthermore, the descriptive statistics revealed substantial variability and risk factors, such as higher claim severity for business-use vehicles and young drivers aged 17–20. The results demonstrate that the truncated Schröter algorithm substantially reduces the execution time while maintaining high accuracy, thus making it a superior tool for risk management and premium setting.

If a sample is designated by a standard sampling strategy and if the character of the study satisfies a predetermined statement for an independent unit in the sample, then the items in the locality remain automatically in the sample. This type of method of selection of sampling units is called adaptive cluster sampling. This manuscript emphasizes the use of the factor-type estimator designed for population mean of the variable under study using the data of highly correlated auxiliary (supplementary) variable under adaptive cluster sampling. The bias, mean squared error and optimum mean squared errors up to the first order is obtained and a simulation study is performed for comparison purpose.

The search for relevant models that can describe the loss data has been one of the main interests of researchers for decades. There is limited research on modeling such data using K-component mixture models. An example of that can be Miljkovic and Grün’s study (2016) of six distributions where they proposed finite mixtures to model the data. In this paper we study two more distributions, namely log-logistic and inverse Weibull distribution in addition of all those proposed by Miljkovic and Grün (2016). We employed the EM algorithm for parameter estimation and then selected the best model using three model selection criteria, namely NLL, AIC and BIC. We also computed the risk measures such as VaR and TVaR and compared them with their empirical counterparts to assess the goodness-of-fit of our proposed models at the extreme quantiles. We found that K-component mixture distribution of loglogistic and inverse Weibull works better than competent models. To get a more generalized view on the theory of mixture distribution, a simulation was carried out, which gave satisfactory results.

The article presents a proposal for a goodness-of-fit test for multivariate normality. The idea of the test is based on the empty cells test, which is well known in the literature. In the empty cells test, the area of the random variable's variability is divided into m disjoint cells. Assuming the truth of hypothesis H0, which proclaims the multivariate normality of the distribution with given parameters, disjoint cells are arranged in such a way that random values with equal probabilities are in each cell. Based on the n-element sample, the number of empty cells, i.e. the cells without any elements from the sample, is determined. Crucial to the proposed procedure is the division of the multidimensional area of variation into disjoint cells. The advantage of this test is that it can be used for relatively small samples. In the article, a simulation comparison of the proposed test's properties and the Kolmogorov-Smirnov test's multivariate version is carried out.

This paper shows how measures of uncertainty from a standard time series model (ARIMA) can be applied to an existing population projection based on components of change using the world as a case study. The measures of forecast uncertainty are relatively easy to calculate and meet several important criteria used by demographers who routinely generate population forecasts. This paper applies the uncertainty measures to a world population forecast based on the Cohort-Component Method. This approach links the probabilistic world forecast uncertainty to the fundamental demographic equation, the cornerstone of demographic theory, which is an important consideration in developing accurate forecasts. The results are compared to the Bayesian probabilistic world forecast developed by the United Nations and found to be similar but show more uncertainty. The results are followed by a discussion suggesting that this new method is well-suited for developing probabilistic world, national, and sub-national population forecasts.

In this paper, we propose a new, four-parameter distribution with increasing, decreasing, bathtub-shaped and a unimodal failure rate, called the Inverse Power Lomax Poisson (IPLP) distribution. The new distribution combines Inverse Power Lomax (IPL) and Poisson distributions. We derive several properties of the new distribution: its probability density function, its reliability and failure rate functions, the quantiles, the stress-strength parameter, complete and incomplete moments, the moment generating function, the probability weighted moment, R?nyi and q-entropies, and order statistics. The study presents the estimation of the model’s parameters based on the maximum likelihood method. The applications of the new distribution are presented using two real data sets, showing its flexibility and potential in modelling lifetime data.