Showing papers on "Kumaraswamy distribution published in 2021"

The Kumaraswamy Generalized Half-Normal Distribution for Skewed Positive Data

Abstract: For the first time, we propose and study the Kumaraswamy generalized half-normal distribution for modeling skewed positive data. The half-normal and generalized half-normal (Cooray and Ananda, 2008) distributions are special cases of the new model. Various of its structural properties are derived, including explicit expressions for the density function, moments, generating and quantile functions, mean deviations and moments of the order statistics. We investigate maximum likelihood estimation of the parameters and derive the expected information matrix. The proposed model is modified to open the possibility that long-term survivors may be presented in the data. Its applicability is illustrated by means of four real data sets.

Kumaraswamy control chart for monitoring double bounded environmental data

Abstract: In this paper, we propose a control chart for monitoring non-normal environmental data. Particularly, we are interested in double bounded data, such as rates and proportions. Control charts based o...

Inference for partially observed competing risks model for Kumaraswamy distribution under generalized progressive hybrid censoring

Abstract: In this paper, inference for a competing risks model is studied when latent failure times follow Kumaraswamy distribution and causes of failure are partially observed. Under generalized progressive...

Evaluation of suitability of wind speed probability distribution models: a case study from Tamil Nadu, India.

Abstract: The optimal design and performance monitoring of wind farms depend on the precise assessment of spatial and temporal distribution of wind speed. The aim of this research is to investigate the appropriateness of nine popular probability distribution models (exponential, gamma, generalised extreme value, inverse Gaussian, Kumaraswamy, log-logistic, lognormal, Nakagami, and Weibull) for the assessment of wind speed distribution (WSD) at 10 sites situated at topographically distinct locations in Tamil Nadu, India, based on 39 years of data. The results suggest that a single distribution cannot produce best fit for all the stations. On an individual level, the generalised extreme value distribution provided the most suitable fit for majority of the stations, followed by the Kumaraswamy distribution. The Kumaraswamy distribution has performed well even if the WSD of the station is negatively skewed. Hence, based on the ranking and performance consistency, the Kumaraswamy distribution can be preferred irrespective of the topographical heterogeneity of the stations.

Multi Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation

Abstract: It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multi reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, R when X,Y, and Z come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of R under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multi stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.

Estimation procedures for Kumaraswamy distribution parameters under adaptive type-II hybrid progressive censoring

Abstract: This paper describes the point and interval estimation of the unknown parameters of Kumaraswamy (Ku) distribution under the adaptive Type-II hybrid progressive censored samples. First, we obtain th...

Estimation of different types of entropies for the Kumaraswamy distribution.

Abstract: The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

A New Generalization of Lehmann Type - II Distribution: Theory, Simulation, and Applications to Survival and Failure Rate data

Abstract: In this paper, a potentiated lifetime model that demonstrates the bathtub-shaped hazard rate function is developed. This proposed model is referred to as Kumaraswamy modified size-biased Lehmann Type-II (Kum–MSBL–II) distribution. Various mathematical and reliability characteristics are derived and discussed. The maximum likelihood estimation method is used to estimate the model parameters and its performance is discussed by following a simulation study. Three-lifetime sets of data are utilized to illustrate the flexibility of the proposed model and the results demonstrate that the proposed model can adequately fit the real-life datasets than the competitors.

A New Family of Generalized Distributions on the Unit Interval: The Family of Distributions

Abstract: The so-called Kumaraswamy distribution is a special probability distribution developed to model doubled bounded random processes for which the mode do not necessarily have to be within the bounds In this article, a generalization of the Kumaraswamy distribution called the T-Kumaraswamy family is defined using the T-R {Y} family of distributions framework The resulting T-Kumaraswamy family is obtained using the quantile functions of some standardized distributions Some general mathematical properties of the new family are studied Five new generalized Kumaraswamy distributions are proposed using the T-Kumaraswamy method Real data sets are further used to test the applicability of the new family

A collection of parametric modal regression models for bounded data.

Abstract: Modal regression is an alternative approach for investigating the relationship between the most likely response and covariates and can hence reveal important structure missed by usual regression me

A new flexible generalized family for constructing many families of distributions

Abstract: We propose a new flexible generalized family (NFGF) for constructing many families of distributions. The importance of the NFGF is that any baseline distribution can be chosen and it does not invol...

Partially constant-stress accelerated life tests model for parameters estimation of Kumaraswamy distribution under adaptive Type-II progressive censoring

Abstract: In a life testing experiments, accelerated life tests (ALTs) model has provided a significant decrease for the cost and time. The problem of statistical inference of constant-stress ALTs based on censored data is discussed in this paper. So, we implement partially constant-stress ALTs model to test units have two parameter Kumaraswamy lifetime population under adaptive Type-II progressive censoring scheme. The population parameters as well as acceleration factor are estimated by using maximum likelihood method for point and interval estimation. Two different confidence intervals are obtained under bootstrap technique. Also, Bayesian approach under different loss functions is used to contract the point and interval estimates of the model parameters with the help of Markov chain Monte Carlo method (MCMC). For illustrative purpose a simulate data set are analyzed. Different developed results discussed in this paper are compared through Monte Carlo simulation study.

Study of a Modified Kumaraswamy Distribution

Abstract: In this article, a structural modification of the Kumaraswamy distribution yields a new two-parameter distribution defined on (0,1), called the modified Kumaraswamy distribution. It has the advantages of being (i) original in its definition, mixing logarithmic, power and ratio functions, (ii) flexible from the modeling viewpoint, with rare functional capabilities for a bounded distribution—in particular, N-shapes are observed for both the probability density and hazard rate functions—and (iii) a solid alternative to its parental Kumaraswamy distribution in the first-order stochastic sense. Some statistical features, such as the moments and quantile function, are represented in closed form. The Lambert function and incomplete beta function are involved in this regard. The distributions of order statistics are also explored. Then, emphasis is put on the practice of the modified Kumaraswamy model in the context of data fitting. The well-known maximum likelihood approach is used to estimate the parameters, and a simulation study is conducted to examine the performance of this approach. In order to demonstrate the applicability of the suggested model, two real data sets are considered. As a notable result, for the considered data sets, statistical benchmarks indicate that the new modeling strategy outperforms the Kumaraswamy model. The transmuted Kumaraswamy, beta, unit Rayleigh, Topp–Leone and power models are also outperformed.

A new probability model for modeling of strength of carbon fiber data: properties and applications

Abstract: The procedures to discover proper new models in probability theory for different data collections are highly prevalent these days among the researchers of this area whenever existing literature models are not appropriate. Before delivering a product, manufacturers of raw materials or finished materials must follow some compliance standards in various engineering disciplines to avoid severe losses. Materials of high strength are necessary to ensure the safety of human lives along with infrastructures to elude the significant obligations linked with the provisions of non-compliant products. Using probability theory, we introduce the weighted version of inverted Kumaraswamy Distribution, which could be considered a better model than some other sub-models used to model Carbon fiber’s strength data. We derive various statistical properties of this distribution such as cumulative distribution, moments, mean residual life, reversed residual life functions, moment generating function, characteristic function, harmonic mean, and geometric mean. Parameters are estimated through the maximum likelihood method and ordinary moments. Simulation studies are carried out to illustrate the theoretical results of these two approaches. Furthermore, two real data sets of Carbon fibers strength are utilized to contrast the proposed model and its sub-models like inverted Kumaraswamy distribution and Kumaraswamy Sushila distribution through different goodness of fit criteria such as Akaike Information Criterion (AIC), corrected Akaike information criterion, and the Bayesian Information Criterion (BIC). Results reveal the outperformance of the proposed model compared to other models, which render it a proper interchange of the current sub-models.

Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

Abstract: Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.

Tail Conditional Expectations Based on Kumaraswamy Dispersion Models

Abstract: Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in housing development, and financial institutions offering loans to small-scale industries. Companies typically face three types of risk (and associated losses from each of these sources): strategic (S); operational (O); and financial (F) (insurance companies additionally face insurance risks) and they come from multiple sources. For asymmetric and bounded losses (properly adjusted as necessary) that are continuous in nature, we conjecture that risk assessment measures via univariate/bivariate Kumaraswamy distribution will be efficient in the sense that the resulting TCE based on bivariate Kumaraswamy type copulas do not depend on the marginals. In fact, almost all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copula’s domain of definition. In this article, we examined the above risk measure in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas. For illustrative purposes, a well-known Stock indices data set was re-analyzed by computing TCE for the bivariate KW type copulas to determine which pairs produce minimum risk in a two-component risk scenario.

Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

Abstract: In this paper, the shape parameters, reliability and hazard rate functions of the exponentiated generalized inverted Kumaraswamy distribution are estimated using Bayesian approach. The Bayes estimators are derived under the squared error loss function and the linear-exponential loss function based on dual generalized order statistics. Credible intervals for the parameters, reliability and hazard rate functions are obtained. The Bayesian prediction (point and interval) for a future observation of the exponentiated generalized inverted Kumaraswamy distribution is obtained based on dual generalized order statistics. All results are specialized to lower record values and a numerical study is presented. Moreover, the theoretical results are applied on three real data sets.

Classical and Bayesian Inference of Conditional Stress-Strength Model under Kumaraswamy Distribution.

Abstract: Stress-strength models have been frequently studied in recent years. An applicable extension of these models is conditional stress-strength models. The maximum likelihood estimator of conditional stress-strength models, asymptotic distribution of this estimator, and its confidence intervals are obtained for Kumaraswamy distribution. In addition, Bayesian estimation and bootstrap method are applied to the model.

Kumaraswamy Distribution Based on Alpha Power Transformation Methods

Abstract: In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

Libby-Novick Kumaraswamy Distribution with Its Properties and Applications

Abstract: The Kumaraswamy distribution is one of the most popular probability distributions with applications to real life data. In this paper, an extension of this distribution called the Libby-Novick Kumaraswamy (LNK) distribution is presented which is believed to provide greater flexibility to model scenarios involving skew-normal data than original one. Analytical expressions for various mathematical properties including its cdf, quantile function, moments, factorial moments, conditional momennts, moment generating function, characteristic function, vitality function, information generating function, reliability measures, mean deviations, mean residual function, Bonferroni and Lorenz Curves are derived.The parameters' estimation of LNK distribution is undertaken using the method of maximum likelihood estimation. A simulation study for different values of sample sizes, to assess the performance of the parameters of LNK distribution is provided. For illustration and performance evaluation of LNK distribution three real-life data sets from the field of engineering and science adapted from earlier studies are used. On comparing the results to previously used methods, LNK distribution shows that it can give consistently better fit than other existing important lifetime models. It is found that the LNK distribution is more suitable and useful to study lifetime data.

Reliability and Inference for Multi State Systems: The Generalized Kumaraswamy Case

Abstract: Semi-Markov processes are typical tools for modeling multi state systems by allowing several distributions for sojourn times. In this work, we focus on a general class of distributions based on an arbitrary parent continuous distribution function G with Kumaraswamy as the baseline distribution and discuss some of its properties, including the advantageous property of being closed under minima. In addition, an estimate is provided for the so-called stress–strength reliability parameter, which measures the performance of a system in mechanical engineering. In this work, the sojourn times of the multi-state system are considered to follow a distribution with two shape parameters, which belongs to the proposed general class of distributions. Furthermore and for a multi-state system, we provide parameter estimates for the above general class, which are assumed to vary over the states of the system. The theoretical part of the work also includes the asymptotic theory for the proposed estimators with and without censoring as well as expressions for classical reliability characteristics. The performance and effectiveness of the proposed methodology is investigated via simulations, which show remarkable results with the help of statistical (for the parameter estimates) and graphical tools (for the reliability parameter estimate).

Estimating the Reliability Function of some Stress- Strength Models for the Generalized Inverted Kumaraswamy Distribution

Abstract: This paper discusses reliability of the stress-strength model The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood, Least Square, and Regression A numerical simulation study a comparison between the three estimators by mean square error is performed It is found that best estimator between the three estimators is Maximum likelihood estimators

Mixed Topp-Leone-Kumaraswamy distribution

Abstract: In this article, a new generalization of the Topp-Leone distribution with a unit interval, namely Mixed Topp-Leone-Kumaraswamy distribution is defined and studied The mathematical properties of this mixing distribution are described Moments, quantile function, R?nyi entropy, incomplete moments and moments of residual are obtained for the new Mixed Topp-Leone - Kumaraswamy distribution The maximum likelihood (MLE), Crans (CM) , Percentile (PM) and Particle Swarm Optimization(PSO) estimators of the parameters are derived The percentile Method is more efficient method as compred to the others Two real data sets are used to illustrate an application and superiority of the proposed distribution

Four Parameters Kumaraswamy Reciprocal Family Of Distributions

Abstract: In this paper, kumaraswamy reciprocal family of distributions is introduced as a new continues model with some of approximation to other probabilistic models as reciprocal, beta, uniform, power function, exponential, negative exponential, weibull, rayleigh and pareto distribution. Some fundamental distributional properties, force of mortality, mills ratio, bowley skewness, moors kurtosis, reversed hazard function, integrated hazard function, mean residual life, probability weighted moments, bonferroni and lorenz curves, laplace-stieltjes transform of this new distribution with the maximum likelihood method of the parameter estimation are studied. Finally, four real data sets originally presented are used to illustrate the proposed estimators.