This paper examines the measurement of extreme poverty in Poland, focusing on the role of equivalence scales. The key research question is whether the original OECD equivalence scale, currently used by Statistics Poland, is consistent with the scale effects implied by the construction of the subsistence minimum across different household types. Using a oneparameter power equivalence scale, extreme poverty rates are recalculated under alternative assumptions based on anonymized microdata from the 2023 Household Budget Survey. The results indicate that the original OECD scale shows stronger economies than the one embedded in the subsistence minimum values, leading to substantial differences in the estimated extreme poverty rate. These findings underline the importance of a careful selection of equivalence scales in official poverty statistics, as methodological choices directly influence poverty assessment and the targeting of social policy.
We examine four two-sided confidence intervals for parameter θ of the Double XShanker distribution: the likelihood-based, Wald-type, bootstrap-t, and the bias-corrected and accelerated (BCa) bootstrap intervals. An explicit expression for the observed Fisher information is derived, allowing theWald interval to be computed directly from the maximum likelihood estimate. Interval performance is evaluated by empirical coverage probability (ECP) and average width (AW) through the Monte Carlo experiments over a range of sample sizes and parameter values. The likelihood-ratio and Wald intervals remain close to the nominal 0.95 level across most settings considered, whereas the bootstrap-t and BCa intervals tend to be narrower but show undercoverage in small samples. An additional sensitivity analysis using B=1000,2000, and 5000 bootstrap resamples indicates that the bootstrap-based conclusions are stable with respect to the number of resamples. The methods are also illustrated using rainfall data from the Los Angeles Civic Center, where the empirical interval estimates are consistent with the simulation findings.
This paper presents a recurrence relation for single and product moments of the Burr-Hatke exponential distribution based on generalized order statistics and record values. Moreover, we have derived the explicit and exact expressions for the single moment of generalized order statistics from the Burr-Hatke exponential distribution. Furthermore, the classical and Bayesian estimation procedures for estimating the Burr-Hatke exponential distribution parameter are discussed when the data are in the form of records and gos. In addition, the asymptotic confidence interval, boot-p confidence interval, and credible interval for the parameter of the Burr-Hatke exponential distribution are discussed. Monte Carlo simulations were conducted to evaluate the performance of the estimators derived from both classical and Bayesian approaches, with a particular emphasis on their mean squared error. Moreover, two real datasets are included for illustrative purposes in this study.
This study develops Bayesian small-area estimates of seat-belt use for Iowa counties from 2017 to 2021. The aim is to produce stable county-by-year estimates and measures of uncertainty for all 99 Iowa counties, although only 15 counties were directly sampled in the Iowa Seat-Belt Use Survey. The analysis focuses on two policy-relevant quantities: the percentage of belted vehicle miles traveled and the percentage of belted vehicle occupants. To address the multivariate, longitudinal, and boundary-inflated structure of the data, we compare several Bayesian hierarchical models for driver and passenger seat-belt-use proportions and combine them with a Poisson log-linear model for occupant counts. Correlated random effects are used to borrow strength across counties, years, and road segments, and posterior inference is implemented using Integrated Nested Laplace Approximations. Model performance is evaluated using WAIC, posterior predictive checks, posterior intervals, Bayesian model averaging, and comparisons with direct estimates. The empirical results show that the Bayesian estimates are generally close to direct estimates in posterior mean, while often producing substantially smaller posterior standard deviations. These gains indicate improved stability for local traffic-safety summaries, although they are interpreted as a bias–variance trade-off rather than as uniform dominance over direct estimation.
We present a new family of distributions (FDs) named the Kumaraswamy type II exponentiated half logistic-G (K-TIIEHL-G). Notably, this FDs can be represented as an infinite linear combination of exponentiated-G densities enabling the derivation of important statistical properties. The density and hazard rate geometries were investigated for some special cases. The model parameters were determined using the maximum likelihood technique and Monte Carlo simulation experiments were carried out to validate the consistency of the model parameters. The Kumaraswamy type II exponentiated half logistic-Weibull (K-TIIEHL-W), a member of the K-TIIEHL-G family, was applied to two sets of real data. The results indicated that the K-TIIEHL-W model significantly outperformed several established contending equi-parameter models in terms of data fitting.
