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In practical scenarios, data measurements like ratios and proportions often fall within the 0 to 1 range, posing unique modeling challenges. While beta and Kumaraswamy distributions are widely used, alternative models often yield better performance, though no clear consensus exists. This paper introduces a new bounded probability distribution based on a transformation of the Weibull distribution, with properties such as moments, entropies, and a quantile function. Additionally, we have developed the sequential probability ratio test (SPRT) for the proposed model. The maximum likelihood estimation method was employed to estimate the model parameters. A Monte Carlo simulation was conducted to evaluate the performance of parameter estimation for the model. Finally, we formulated a quantile regression model and applied it to data sets related to risk assessment and educational attainment, demonstrating its superior performance over alternative regression models. These results highlight the importance of our contributions to enhancing the statistical toolkit for analyzing bounded variables across different scientific fields.

This research is centered on exploring a mathematically tractable and versatile family of probability distributions, specifically focusing on one family member. We have used the exponential distribution as a base distribution to create a novel distribution, which we have aptly named the “New Odd-type Exponential Distribution.” In this paper, we provide an overview of the essential characteristics inherent to this innovative distribution. This model showcases a variety of hazard functions, including the reverse-J, decreasing, constant, increasing and constant, bathtub, and S-shaped shapes. The estimation of the distribution’s parameters is conducted through both classical and Bayesian methods. We validate the accuracy of the classical estimation procedure through simulation studies. These simulations demonstrate a reduction in biases and mean square errors as sample sizes increase, even for smaller samples. To showcase the practicality of the proposed distribution, we apply it to two sets of real-world data, employing both classical and Bayesian approaches. We evaluate the performance of our suggested distribution model using various model selection criteria and goodness-of-fit test statistics. Empirical evidence from these evaluations confirms that our proposed model surpasses some existing models in the literature. Further, the suggested model was analyzed using the Bayesian approach and the Hamiltonian Monte Carlo method. Its predictive capability was also explored by using the posterior predictive checks, and it can predict the data consistently.

The present article presents a novel two-parameter distribution called inverse unit compound Rayleigh distribution (IUCRD), which has the support (1, ). It is propounded via the inverse transformation of the unit compound Rayleigh distribution (UCRD). Different properties of the IUCRD, namely, the quantile function, the mode, stochastic ordering, moments, and heavy-tailedness, among others, are explored. We notice that the distribution PDF is either unimodal or nonincreasing. It can also be left-skewed or right-skewed, depending on the values of the parameters of the IUCRD. The graph of the hazard rate function of the IUCRD is the upside-down bathtub shape or nondecreasing. Heavy-tailedness is also among the properties of the IUCRD determined in this work. We provide evidence of the relationship between the IUCRD and exponential distribution via the derivation of distributions of certain functions of one variable. Sixteen different estimation methods are compared employing the Monte Carlo simulation procedure. Numerical simulation evidence attests to the KE method being the best estimation methodology for the parameters of the IUCRD. Interestingly, according to the simulation results, the ML procedure assumes the second position. In demonstrating the usefulness of the IUCRD, we use the ML technique to fit the distribution to five real-world datasets and compare its fits with the fits of seven existing distributions to the data by employing goodness of fit statistics. For each of the data, the minimum value of each of the statistics corresponds to the IUCRD. This result makes it clear that in many data analysis circumstances, the IUCRD can be preferable to several continuous distributions, especially the UCRD and the inverse unit exponential, inverse Weibull, inverse Rayleigh, inverse Chen, inverse exponential, and inverse exponential distributions.

This research introduces a novel two-parameter distribution, the power-modified XLindley distribution, developed through the application of power transformation techniques to the existing modified XLindley distribution. This new distribution enhances flexibility and adaptability in statistical modeling. We conduct a thorough examination of its statistical properties, exploring its potential to improve data fitting and modeling accuracy. To assess the effectiveness of the model, we employ multiple estimation techniques and evaluate their performance through extensive simulation experiments. Our findings indicate that the maximum product of the spacings method is particularly effective for parameter estimation. To demonstrate the practical utility of the proposed model, we apply it to two real-world datasets: one related to flood data and the other to reliability engineering. The results underscore the distribution’s superior ability to capture the characteristics of these datasets compared to existing models, highlighting its significance for applications in natural disaster analysis and reliability studies.

In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and properties of the family are provided in a general form. A specific sub-model alpha-sine Weibull of this family is also introduced using the Weibull distribution as a parent distribution and studied deeply. The statistical properties of this new distribution are investigated and intended parameters are estimated using the maximum likelihood, maximum product of spacings, least square, weighted least square, and minimum distance methods. For further justification of these estimates, a simulation experiment is carried out. Two real data sets are analyzed to show the suggested model’s application. The suggested model performed well compares to some existing models considered in the study.

This study introduces a novel family of probability distributions, termed the Pi-Power Logistic-G family, constructed through the application of the Pi-power transformation technique. By employing the Weibull distribution as the baseline generator, a new and flexible model, the Pi-Power Logistic Weibull distribution, is formulated. Particular emphasis is given to this specific member of the family, which demonstrates a rich variety of hazard rate shapes, including J-shaped, reverse J-shaped, and monotonic increasing patterns, thereby highlighting its adaptability in modeling diverse types of lifetime data. The paper examines the fundamental properties of this distribution and applies the method of maximum likelihood estimation (MLE) to determine its parameters. A Monte Carlo simulation was performed to assess the performance of the estimation method, demonstrating that both Bias and mean square error decline as the sample size increases. The utility of the proposed distribution is further highlighted through its application to real-world engineering datasets. Using model selection metrics and goodness-of-fit tests, the results demonstrate that the proposed model outperforms existing alternatives. In addition, a Bayesian approach was used to estimate the parameters of both datasets, further extending the model’s applicability. The findings of this study have significant implications for the fields of reliability modeling, survival analysis, and distribution theory, enhancing methodologies and offering valuable theoretical insights.

ABSTRACT This study introduces the power odd Lindley half‐logistic distribution (POLiHLD), a novel statistical distribution developed to provide enhanced flexibility for modeling diverse data sets. This distribution is derived by combining the characteristics of the odd Lindley and half‐logistic distributions through the power transformation, resulting in a model capable of capturing various shapes and tail behaviors. We explore the fundamental statistical properties of the POLiHLD, including moments and moment‐generating functions, a sequential probability ratio test, and average sample number, among others. Extensive simulation studies were conducted to validate the estimation method used to estimate the parameters of the developed distribution. These simulations highlight the robustness of the estimation method used. The POLiHLD's flexibility is shown through its fitting to two real datasets: the first data set represents the ordered failure of components, and the second data set captures economic data. Comparative analyses with existing distributions show that the POLiHLD provides a better fit for the analyzed datasets. A regression model was developed to ascertain the predictive ability of the proposed model. Different shapes of the PDF for the POLiHLD.

ABSTRACT Ranked set sampling (RSS) is an efficient sampling method when ranking observations is easier than precise measurement. Unlike simple random sampling (SRS), RSS can reduce costs. The unit Xgamma distribution (UXGD), defined over the interval (0,1), effectively captures the characteristics of negatively skewed datasets. This study aims to comprehensively compare several estimation methods, including maximum likelihood, Anderson‐Darling, Kolmogorov, ordinary least squares, Anderson‐Darling left tail second order, Cramer‐von‐Mises, left tail Anderson‐Darling, weighted least squares, maximum product spacing, right tail Anderson‐Darling, and five types of minimum spacing distance for the UXGD parameter under both RSS and SRS techniques. Through extensive simulations, we evaluate the performance of these estimators using multiple criteria under both designs. We rank the estimators based on their performance under both sampling schemes. Simulation findings indicate that the maximum product spacing and maximum likelihood estimation methods are superior to alternative approaches for assessing the estimated quality of RSS and SRS, respectively. It is interesting to note that for both SRS and RSS datasets, the estimates revealed by our model satisfy the consistency property. With an increase in the sample size, the estimates approach the true parameter values. Furthermore, the results highlight the efficiency gains of RSS over SRS, as evidenced by improved accuracy metrics. Two real‐world applications, including COVID‐19 data from the United Kingdom and France, demonstrate the practical utility of our findings. Ranked set sampling (RSS) is an efficient sampling method when ranking observations is easier than precise measurement. Unlike simple random sampling, RSS can reduce costs. The unit Xgamma distribution, defined over the interval (0,1), effectively captures the characteristics of negatively skewed datasets.

ABSTRACT This paper proposes a novel form of the unit new XLindley distribution, which is derived by incorporating the idea of inverse transformation of the cumulative distribution function. The derived distribution is defined on the positive real line (0,∞)$$ \\left(0,\\infty \\right) $$ and it exhibits a different range of shapes. We also discuss some important statistical properties of the proposed model, including moments, moment‐generating function, survival and hazard rate functions, quantiles, order statistics, etc., to present a comprehensive theoretical framework. In addition to these, fifteen different estimation methods are employed for conducting the parameter estimation for the new distribution. Besides, a simulation study is performed to evaluate their behaviors using some measures like bias, mean squared error, relative error, and absolute differences. Besides, the usefulness and utility of the newly proposed distribution are checked through real‐life applications via some practical datasets. This practical application is conducted by comparing the new distribution with some other existing counterparts in terms of the value of some model selection criterion. This paper proposes a novel form of the unit new XLindley distribution, which is derived by incorporating the idea of reciprocal transformation of the cumulative distribution function. The derived distribution is defined on the positive real line (0, infty) and it exhibits a different range of shapes. We also discuss some important statistical properties of the proposed model, including moments, moment‐generating function, survival and hazard rate functions, quantiles, order statistics, etc., to present a comprehensive theoretical framework. In addition to these, fifteen different estimation methods are employed for conducting the parameter estimation for the new distribution. Besides, a simulation study is performed to evaluate their behaviors using some measures like bias, mean squared error, relative error, and absolute differences. Besides, the usefulness and utility of the newly proposed distribution are checked through real‐life applications via some practical datasets. This practical application is conducted by comparing the new distribution with some other existing counterparts in terms of the value of some model selection criterion.

ABSTRACT This article introduces a two‐parameter statistical model derived by applying an inverse transformation to the cumulative distribution function of the Pham distribution. The proposed model offers a flexible and tractable framework for modeling skewed and heavy‐tailed data, making it well‐suited for applications in reliability engineering, survival analysis, and related fields. We derive key statistical properties of the model, including the quantile function, moments, and the moment‐generating function. Furthermore, we assess the performance of fifteen different estimation methods through extensive simulations to identify the most efficient techniques for parameter estimation. The practical utility of the proposed model is demonstrated using real‐life datasets, where it outperforms several existing competing models. Also, Bayesian inference is implemented in the application section to provide a more comprehensive analysis. The results underscore the model's flexibility, robustness, and computational efficiency in real‐world settings. This article introduces a two‐parameter statistical model derived by applying an inverse transformation to the cumulative distribution function of the Pham distribution. The proposed model offers a flexible and tractable framework for modeling skewed and heavy‐tailed data, making it well‐suited for applications in reliability engineering, survival analysis, and related fields. We derive key statistical properties of the model, including the quantile function, moments, and the moment‐generating function. Furthermore, we assess the performance of fifteen different estimation methods through extensive simulations to identify the most efficient techniques for parameter estimation. The practical utility of the proposed model is demonstrated using real‐life datasets, where it outperforms several existing competing models. Also, Bayesian inference is implemented in the application section to provide a more comprehensive analysis. The results underscore the model's flexibility, robustness, and computational efficiency in real‐world settings.