Search Results (21)

This study analyzes the factors influencing the proportions of blank and null votes in Brazilian municipalities during the 2018 presidential elections. The behavior of the variable of interest is examined using unit regression models within the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework. Specifically, five different unit regression models are explored, beta, simplex, Kumaraswamy, unit Weibull, and reflected unit Burr XII regressions, each incorporating submodels for both indexed distribution parameters. The beta regression model emerges as the best fit through rigorous model selection and diagnostic procedures. The findings reveal that the disaggregated municipal human development index (MHDI), particularly its income, longevity, and education dimensions, along with the municipality’s geographic region, significantly affect voting behavior. Notably, higher income and longevity values are linked to greater proportions of blank and null votes, whereas the educational level exhibits a negative relationship with the variable of interest. Additionally, municipalities in the Southeast region tend to have higher average proportions of blank and null votes. In terms of variability, the ability of a municipality’s population to acquire goods and services is shown to negatively influence the dispersion of vote proportions, while municipalities in the Northeast, North, and Southeast regions exhibit distinct patterns of variation compared to other regions. These results provide valuable insights into electoral participation’s socioeconomic and regional determinants, contributing to broader discussions on political engagement and democratic representation in Brazil. Full article

A novel odd generalized exponential Kumaraswamy–Weibull distribution is defined. This distribution is distinguished by its capacity to capture a wider class of hazard functions than the standard Weibull models, such as non-monotonic and bathtub-shaped hazards. This is an advancement in distribution theory because it provides a new simplified form of the distribution with a much more complicated behavior, which results in better statistical inference and detail in survival analysis and other related fields. Considerations on the identifiability of the proposed distribution are addressed, emphasizing the distinct contributions of its parameters and their roles in model behavior characterization. One real dataset from a survival experiment is considered, highlighting the practical implications of our distribution in the context of reliability. Full article

Latin America was one of the hotspots of COVID-19 during the pandemic. Therefore, understanding the COVID-19 mortality rate in Latin America is crucial, as it can help identify at-risk populations and evaluate the quality of healthcare. In an effort to find a more flexible and suitable model, this work formulates a new quantile regression model based on the unit ratio-Weibull (URW) distribution, aiming to identify the factors that explain the COVID-19 mortality rate in Latin America. We define a systematic structure for the two parameters of the distribution: one represents a quantile of the distribution, while the other is a shape parameter. Additionally, some mathematical properties of the new regression model are presented. Point and interval estimates of maximum likelihood in finite samples are evaluated through Monte Carlo simulations. Diagnostic analysis and model selection are also discussed. Finally, an empirical application is presented to understand and quantify the effects of economic, social, demographic, public health, and climatic variables on the COVID-19 mortality rate quantiles in Latin America. The utility of the proposed model is illustrated by comparing it with other widely explored quantile models in the literature, such as Kumaraswamy and unit Weibull regressions. Full article

Floating photovoltaic systems (FPVSs) are gaining popularity, especially in countries with high population density and abundant solar energy resources. FPVSs provide a variety of advantages, particularly in situations where land is limited. Therefore, the main objective of the study is to evaluate the solar energy potential and investigate the techno-economic perspective of FPVSs at 15 water reservoirs in Northern Cyprus for the first time. Due to the solar radiation variations, solar power generation is uncertain; therefore, precise characterization is required to manage the grid effectively. In this paper, four distribution functions (Johnson SB, pert, Phased Bi-Weibull, and Kumaraswamy) are newly introduced to analyze the characteristics of solar irradiation, expressed by global horizontal irradiation (GHI), at the selected sites. These distribution functions are compared with common distribution functions to assess their suitability. The results demonstrated that the proposed distribution functions, with the exception of Phased Bi-Weibull, outperform the common distribution regarding fitting GHI distribution. Moreover, this work aims to evaluate the effects of floating photovoltaic systems on water evaporation rates at 15 reservoirs. To this aim, five methods were used to estimate the rate of water evaporation based on weather data. Different scenarios of covering the reservoir’s surface with an FPVS were studied and discussed. The findings showed that annual savings at 100% coverage can reach 6.21 $\times$ 10⁵ m³ compared to 0 m³ without PV panels. Finally, technical and economic assessment of FPVSs with various scales, floating assemblies, and PV technologies was conducted to determine the optimal system. The results revealed that a floating structure (North orientation-tilt 6°) and bifacial panels produced the maximum performance for the proposed FPVSs at the selected sites. Consequently, it is observed that the percentage of reduction in electricity production from fossil fuel can be varied from 10.19% to 47.21% at 75% FPV occupancy. Full article

This paper introduces a flexible three-parameter extension of the Lomax model called the odd Lomax–Lomax (OLxLx) distribution. The OLxLx distribution can provide left-skewed, symmetrical, right-skewed, and reversed-J shaped densities and increasing, constant, unimodal, and decreasing hazard rate shapes. Some mathematical properties of the introduced model are derived. The OLxLx density can be expressed as mixture of Lomax densities. The OLxLx parameters are estimated by using eight estimation methods and their performance is explored by using detailed simulation studies. The partial and overall ranks of the mean relative errors, absolute biases, and mean square errors of different estimators are presented to choose the best estimation method. The flexibility and applicability of the OLxLx distribution is shown using real-life medicine data, illustrating the superior fit of the OLxLx distribution over other competing Lomax distributions. The OLxLX distribution outperforms some rival Lomax distributions including the Kumaraswamy–Lomax, McDonald–Lomax, Weibull–Lomax, transmuted Weibull–Lomax, exponentiated-Lomax, Lomax–Weibull, modified Kies–Lomax, Burr X Lomax, beta exponentiated-Lomax, odd exponentiated half-logistic Lomax, and transmuted-Lomax distributions, among others. Full article

In this article, an attempt is made to propose a novel method of lifetime distributions with maximum flexibility using a popular T–X approach together with an exponential distribution, which is known as the New Generalized Logarithmic-X Family (NGLog–X for short) of distributions. Additionally, the generalized form of the Weibull distribution was derived by using the NGLog–X family, known as the New Generalized Logarithmic Weibull (NGLog–Weib) distribution. For the proposed method, some statistical properties, including the moments, moment generating function (MGF), residual and reverse residual life, identifiability, order statistics, and quantile functions, were derived. The estimation of the model parameters was derived by using the well-known method of maximum likelihood estimation (MLE). A comprehensive Monte Carlo simulation study (MCSS) was carried out to evaluate the performance of these estimators by computing the biases and mean square errors. Finally, the NGLog–Weib distribution was implemented on four real biomedical datasets and compared with some other distributions, such as the Alpha Power Transformed Weibull distribution, Marshal Olkin Weibull distribution, New Exponent Power Weibull distribution, Flexible Reduced Logarithmic Weibull distribution, and Kumaraswamy Weibull distribution. The analysis results demonstrate that the new proposed model performs as a better fit than the other competitive distributions. Full article

In this study, we propose a new three-parameter lifetime model based on the type-I half-logistic G family and the unit-Gompertz model, which we named the half-logistic unit Gompertz type-I distribution. The key feature of such a novel model is that it adds a new tuning parameter to the unit-Gompertz model using the type-I half-logistic family in order to make the unit-Gompertz model more flexible. Diagrams and numerical results are used to look at the new model’s mathematical and statistical aspects. The efficiency of estimating the distribution parameters is measured using a variety of well-known classical methodologies, including Anderson–Darling, maximum likelihood, least squares, weighted least squares, right tail Anderson–Darling, and Cramer–von Mises estimation. Finally, using the maximum likelihood estimation method, the flexibility and ability of the proposed model are illustrated by means of re-analyzing two real datasets, and comparisons are provided with the fit accomplished by the unit-Gompertz, Kumaraswamy, unit-Weibull, and Kumaraswamy beta distributions for illustrative purposes. Full article

In this paper, we will present a new, more flexible class of distributions with a domain in the interval (0,1), which presents heavier tails than other distributions in the same domain, such as the $Beta$, Kumaraswamy, and Weibull Unitary distributions. This new distribution is obtained as a transformation of two independent random variables with a Weibull distribution, which we will call the Generalized Unitary Weibull distribution. Considering a particular case, we will obtain an alternative to the $Beta$, Kumaraswamy, and Weibull Unitary distributions. We will call this new distribution of two parameters the type 2 unitary Weibull distribution. The probability density function, cumulative probability distribution, survival function, hazard rate, and some important properties that will allow us to infer are provided. We will carry out a simulation study using the maximum likelihood method and we will analyze the behavior of the parameter estimates. By way of illustration, real data will be used to show the flexibility of the new distribution by comparing it with other distributions that are known in the literature. Finally, we will show a quantile regression application, where it is shown how the proposed distribution fits better than other competing distributions for this type of application. Full article

Probability distributions perform a very significant role in the field of applied sciences, particularly in the field of reliability engineering. Engineering data sets are either negatively or positively skewed and/or symmetrical. Therefore, a flexible distribution is required that can handle such data sets. In this paper, we propose a new family of lifetime distributions to model the aforementioned data sets. This proposed family is known as a “New Modified Exponent Power Alpha Family of distributions” or in short NMEPA. The proposed family is obtained by applying the well-known T-X approach together with the exponential distribution. A three-parameter-specific sub-model of the proposed method termed a “new Modified Exponent Power Alpha Weibull distribution” (NMEPA-Wei for short), is discussed in detail. The various mathematical properties including hazard rate function, ordinary moments, moment generating function, and order statistics are also discussed. In addition, we adopted the method of maximum likelihood estimation (MLE) for estimating the unknown model parameters. A brief Monte Carlo simulation study is conducted to evaluate the performance of the MLE based on bias and mean square errors. A comprehensive study is also provided to assess the proposed family of distributions by analyzing two real-life data sets from reliability engineering. The analytical goodness of fit measures of the proposed distribution are compared with well-known distributions including (i) APT-Wei (alpha power transformed Weibull), (ii) Ex-Wei (exponentiated-Weibull), (iii) classical two-parameter Weibull, (iv) Mod-Wei (modified Weibull), and (v) Kumar-Wei (Kumaraswamy–Weibull) distributions. The proposed class of distributions is expected to produce many more new distributions for fitting monotonic and non-monotonic data in the field of reliability analysis and survival analysis. Full article

In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions. Full article

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models. Full article

The estimation of the unknown parameters of Type II Half Logistic Weibull (TIIHLW) distribution was analyzed in this paper. The maximum likelihood and Bayes methods are used as estimation methods. These estimators are used to estimate the fuzzy reliability function and to choose the best estimator of the fuzzy reliability function by comparing the mean square error (MSE). The simulation’s results showed that fuzziness is better than reality for all sample sizes, and fuzzy reliability at Bayes predicted estimates is better than the maximum likelihood technique. It produces the lowest average MSE until a sample size of n = 50 is obtained. A simulated data set is applied to diagnose the performance of the two techniques applied here. A real data set is used as a practice for the model discussed and developed the maximum likelihood estimate alternative model of TIIHLW as Topp Leone inverted Kumaraswamy, modified Kies inverted Topp–Leone, Kumaraswamy Weibull–Weibull, Marshall–Olkin alpha power inverse Weibull, and odd Weibull inverted Topp–Leone. We conclude that the TIIHLW is the best distribution fit for this data. Full article

We propose a new generator for unit interval which is used to establish univariate and bivariate families of distributions. The univariate family can serve as an alternate to the Kumaraswamy-G univariate family proposed earlier by Cordeiro and de-Castro in 2011. Further, the new generator can also be used to develop more alternate univariate and bivariate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G and Transmuted-G for support (0, 1). Some structural properties of the univariate family are derived and the estimation of parameters is dealt. The properties of a special model of this new univariate family called a New Kumaraswamy-Weibull (NKwW) distribution are obtained and parameter estimation is considered. A Monte Carlo simulation is reported to assess NKwW model parameters. The bivariate extension of the family is proposed and the estimation of parameters is described. The simulation study is also conducted for bivariate model. Finally, the usefulness of the univariate NKwW model is illustrated empirically by means of three real-life data sets on Air Conditioned Failures, Flood and Breaking Strength of Fibers, and one real-life data on UEFA Champion’s League for bivariate model. Full article

The Vasicek distribution is a two-parameter probability model with bounded support on the open unit interval. This distribution allows for different and flexible shapes and plays an important role in many statistical applications, especially for modeling default rates in the field of finance. Although its probability density function resembles some well-known distributions, such as the beta and Kumaraswamy models, the Vasicek distribution has not been considered to analyze data on the unit interval, especially when we have, in addition to a response variable, one or more covariates. In this paper, we propose to estimate quantiles or means, conditional on covariates, assuming that the response variable is Vasicek distributed. Through appropriate link functions, two Vasicek regression models for data on the unit interval are formulated: one considers a quantile parameterization and another one its original parameterization. Monte Carlo simulations are provided to assess the statistical properties of the maximum likelihood estimators, as well as the coverage probability. An R package developed by the authors, named vasicekreg, makes available the results of the present investigation. Applications with two real data sets are conducted for illustrative purposes: in one of them, the unit Vasicek quantile regression outperforms the models based on the Johnson-SB, Kumaraswamy, unit-logistic, and unit-Weibull distributions, whereas in the second one, the unit Vasicek mean regression outperforms the fits obtained by the beta and simplex distributions. Our investigation suggests that unit Vasicek quantile and mean regressions can be of practical usage as alternatives to some well-known models for analyzing data on the unit interval. Full article

Although there are many continuous distributions in the literature, only a handful take advantage of the modeling power provided by trigonometric functions. To our knowledge, none of them are based on the so-called secant function, defined as the reciprocal of the cosine function. The secant function can go to large values whenever the cosine function goes to small values. The idea is to profit from this trigonometric property to modify well-known distribution tails and overall skewness features. With this in mind, in this paper, a new class of trigonometric distributions based on the secant function is introduced. It is called the Sec-G class. We discuss the main mathematical characteristics of this class, including series expansions of the corresponding cumulative distribution and probability density functions, as well as several probabilistic measures and functions. In particular, we present the moments, skewness, kurtosis, Lorenz, and Bonferroni curves, reliability coefficient, entropy measure, and order statistics. Throughout the study, emphasis is placed on the unique four-parameter continuous distribution of this class, defined with the Kumaraswamy-Weibull distribution as the baseline. The estimation of the model parameters is performed using the maximum likelihood method. We also carried out a numerical simulation study and present the results in graphic form. Three referenced datasets were analyzed, and it is proved that the proposed secant Kumaraswamy-Weibull model outperforms important competitors, including the Kumaraswamy-Weibull, Kumaraswamy-Weibull geometric, Kumaraswamy-Weibull Poisson, Kumaraswamy Burr XII, and Weibull models. Full article