Kumaraswamy distribution

About: Kumaraswamy distribution is a research topic. Over the lifetime, 213 publications have been published within this topic receiving 3393 citations. The topic is also known as: Kumaraswamy's double bounded distribution.

Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

Abstract: In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.

On some properties of Generalized Transmuted Kumaraswamy distribution

Abstract: This articles introduces a new lifetime model called the generalized transmuted Kumaraswamy distribution which extends the Kumaraswamy distribution from the family proposed by Nofal et al., (2017). We provide hazard and survival functions of the proposed distribution. The statistical properties of the proposed model are provided and the method of Maximum Likelihood Estimation (MLE) was proposed in estimating its parameters.

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Kumaraswamy Distribution

Abstract: In this paper, differential calculus was used to obtain the ordinary differential equations (ODE) of the probability density function (PDF), Quantile function (QF), survival function (SF), inverse survival function (ISF), hazard function (HF) and reversed hazard function (RHF) of Kumaraswamy distribution. The parameters and support that define the distribution inevitably determine the nature, existence, uniqueness and solution of the ODEs. The method can be extended to other probability distributions, functions and can serve an alternative to estimation and approximation. Computer codes and programs can be developed and used for the implementation.

Inference on the log-exponentiated Kumaraswamy distribution

Abstract: In this paper, the log-exponentiated Kumaraswamy (LEK) distribution is introduced and studied as a survival model of unemployment, its survived function has the interesting property that it can be decreasing depending on the shape parameters. The method of maximum likelihood is applied for estimating the model parameters, survival and hazard rate functions. Stratification is used to reduce heterogeneity in survival unemployment data. To achieve this aim, three models are considered. In the first model, unemployment experience for all working ages (15 – 60) is studied. In the second model, unemployment experience for ages (30-60) is studied and in the third model, unemployment experience for ages (45-60) is studied. Unemployment is modeled as a function of age. The distribution of unemployment with respect to age is represented by the LEK distribution or the three suggested models. For different values of samples sizes, Monte Carlo simulation is performed to investigate the precision of maximum likelihood estimates.