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A new distribution is proposed for modeling lifetime data. It has better hazard rate properties than the gamma, lognormal and the Weibull distributions. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A real data example is discussed to illustrate its applicability.

Wind direction and speed are both crucial factors for wind farm layout; however, the relationship between the two factors has not been well addressed. To optimize wind farm layout, this study aims to statistically explore wind speed characteristics under different wind directions and wind direction characteristics. For this purpose, the angular–linear model for approximating wind direction and speed characteristics were adopted and constructed with specified marginal distributions. Specifically, Weibull–Weibull distribution, lognormal–lognormal distribution and Weibull–lognormal distribution were applied to represent the marginal distribution of wind speed. Moreover, the finite mixture of von Mises function (FVMF) model was used to investigate the marginal distribution of wind direction. The parameters of those models were estimated by the expectation–maximum method. The optimal model was obtained by comparing the coefficient of determination value (R2) and Akaike’s information criteria (AIC). In the numerical study, wind data measured at a featured wind farm in north China was adopted. Results showed that the proposed joint distribution function could accurately represent the actual wind data at different heights, with the coefficient of determination value (R2) of 0.99.

In unsaturated soil mechanics, the soil–water characteristic curve (SWCC) is the most fundamental soil attribute. All seepage analyses require SWCC to generate the pore-water pressure and water content distribution within the soil layers. SWCC is often determined using laboratory procedures. However, the expensive cost, long testing time, and difficulty of the SWCC tests hinder the use of unsaturated soil mechanics in engineering practice. Models for predicting SWCC have been proposed in the literature; however, the equations cannot be applied to soils of a wide variety, and their parameters lack physical significance. This work used a modified lognormal distribution function to generate the equations that best suit the grain-size distribution (GSD) and the model that estimates SWCC for a wide range of soil types. The parameters of the proposed GSD equation have well-defined physical meanings. The model for estimating SWCC was established based on the link between soil pore-size distribution and dry density, void ratio, and saturated water content. The air-entry value of coarse-grained soil is a function of inflection point of SWCC and percentage of coarse particle. The air-entry value of fine-grained soil is a function of saturated water content. Experiments were carried out as part of this study to evaluate the proposed equation as well as its model. The proposed model to estimate SWCC was compared with other models. The proposed model is better than other models in the estimation of SWCC from GSD.

Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed κ-Weibull distribution and weakest-link scaling theory, which makes the κ-Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the κ-lognormal probability distribution and calculate the generalized (power) mean of κ-lognormal variables. The κ-lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the κ-deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions.

Survival and reliability analyses deal with incomplete failure time data, such as censored and truncated data. Recently, the classical left-truncation scheme was generalized to analyze “field data”, defined as samples collected within a fixed period. However, existing competing risks models dealing with left-truncated field data are not flexible enough. We propose copula-based competing risks models for latent failure times, permitting a flexible parametric form. We formulate maximum likelihood estimation methods under the Weibull, lognormal, and gamma distributions for the latent failure times. We conduct simulations to check the performance of the proposed methods. We finally give a real data example. We provide the R code to reproduce the simulations and data analysis results.

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages.

In probabilistic modeling across engineering, finance, and telecommunications, sums of lognormal random variables frequently occur, yet no closed-form expression exists for their distribution. This study systematically evaluates three approximation methods-Wilkinson (W), Schwartz & Yeh (SY), and Inverse (I)-for correlated lognormal variates across varying sample sizes and correlation structures. Using Monte Carlo simulations with 5, 15, 25, and 30 samples and correlation coefficients of 0.3, 0.6, and 0.9, we compared Type I error rates through Anderson-Darling goodness-of-fit tests. Our findings demonstrate that the Wilkinson approximation consistently outperforms the other methods for correlated variates, exhibiting the lowest Type I error rates across all tested scenarios. This contradicts some previous findings in telecommunications literature where SY was preferred. We validated these results using real-world datasets from engineering (fatigue life of ball bearings) and finance (stock price correlations), confirming the Wilkinson approximation's superior performance through probability density function comparisons. This research provides practical guidance for selecting appropriate approximation methods when modeling correlated lognormal sums in diverse applications.

The article identifies the social structure of the Russian society by the level of material security. The research results proceed from the early authors’ studies on the analysis of the inequality of population distribution according to certain components of material security (income and housing security). The subject matter of this study was to identify the scale of social groups in the two-criteria model of social structure by the level of cash income and housing security. We proceeded from the hypothesis that compared with the single-criteria model of social structure, representing the integral distribution by the level of material security, its two-criteria model reveals social groups that significantly vary by the scale. The article presents the updated criteria of material security. We used these criteria to form social structure models. To update the criteria, we used mathematical models and informative indicators, which allowed to clarify the quantitative requirements for the level of cash income and housing parameters. Moreover, we relied on the foreign and domestic experience of research and development on this issue. However, we present for the first time a two-criteria model of the social structure of the Russian society by the level of material security based on the updated standards. For assessments and forming this model of social structure, we used the official statistics and the Russia Longitudinal Monitoring Survey, RLMS — HSE. The results can be applied in the development of targeted social policy measures, as well as may be in demand for further theoretical and methodological substantiation and practical research on material security and identification of social structures.

Modeling groundwater properties is an important tool by means of which water resources management can judge whether these properties are within the safe limits or not. This is usually done regularly and in the aftermath of crises that are expected to reflect negatively on groundwater properties, as occurred in Jordan due to crises in neighboring countries. In this study, specific capacity and salinity of groundwater of B2/A7 aquifer in Amman Zarqa Basin were evaluated to figure out the effect of population increase in this basin as a result of refugee flux from neighboring countries to this heavily populated basin after Gulf crises 1990 and 2003. Both properties were found to exhibit a three-parameter lognormal distribution. The empirically calculated β parameter of this distribution mounted up to 0.39 m³/h/min for specific capacity and 238 ppm for salinity. This parameter is suggested to account for the global changes that took place all over the basin during the entire period of observation and not for local changes at every well or at certain localities in the basin. It can be considered as an exploratory result of data analysis. Formal and implicit evaluation followed this step using structural analysis and construction of experimental semivariograms that represent the spatial variability of both properties. The adopted semivariograms were then used to construct maps to illustrate the spatial variability of the properties under consideration using kriging interpolation techniques. Semivariograms show that specific capacity and salinity values are spatially dependent within 14,529 and 16,309 m, respectively. Specific capacity semivariogram exhibit a nugget effect on a small scale (324 m). This can be attributed to heterogeneity or inadequacies in measurement. Specific capacity and salinity maps show that the major changes exhibit a northwest southeast trend, near As-Samra Wastewater Treatment Plant. The results of this study suggest proper management practices.