On Estimation and Prediction for the Inverted Kumaraswamy Distribution Based on General Progressive Censored Samples

Abstract

In this article, the problem of estimating unknown parameters of the inverted kumaraswamy (IKum) distribution is considered based on general progressive Type-II censored Data. The maximum likelihood (MLE) estimators of the parameters are obtained while the Bayesian estimates are obtained using the squared error loss(SEL) as symmetric loss function. Also we used asymmetric loss functions as the linear-exponential loss (LINEX), generalized entropy (GE) and Al-Bayatti loss function (AL-Bayatti). Lindely's approximation method is used to evaluate the Bayes estimates. We also derived an approximate confidence interval for the parameters of the inverted Kumaraswamy distribution. Two-sample Bayesian prediction intervals are constructed with an illustrative example. Finally, simulation study concerning different sample sizes and different censoring schemes were reported.

Statistical Inference under Censored Data for the New Exponential‐X Fréchet Distribution: Simulation and Application to Leukemia Data

“…(1) First derive the log-product equation (33) (2) Find the partial derivative for equation (33), with respect to each existing parameter, respectively (3) We all know that these equations are extremely tough to solve, so we will start here by using nonlinear optimisation algorithms such as the Newton-Raphson algorithm takes a role in solving these kinds of problems…”

“…In this case, the model can be known as a Type-I censoring model (see Balakrishnan and Aggarwala [ 23 ]). For more examples of censored sampling based on different schemes, see [ 24 – 33 ].…”

“…en, the number of units that fail by time T, say m, is a random variable, where m < n. e lifetimes of the initial m failures are determined, as well as the lifetimes of the subsequent m failures of the remaining n − m units are censored, where all that is known is that they will be greater than T. In this case, the model can be known as a Type-I censoring model (see Balakrishnan and Aggarwala [23]). For more examples of censored sampling based on different schemes, see [24][25][26][27][28][29][30][31][32][33].…”

Multicomponent stress-strength reliability based on a right long-tailed distribution

“…The alpha, beta, and theta are initial values for the parameters. [ 1 ] , e s t i m a t i o n $par [ 2 ] , e s t i m a t i o n $par [ 3 ] ) return ( out ) }…”

“…The curves for pdf and hazard rate function (hrf) of the IKu distribution reveal decreasing (monotonic) and upside-down bathtub (non-monotonic) shapes (Figures 1 and 2). The estimation and prediction problems of this distribution based on general progressive censored samples were considered in [2]. A generalized version of the IKu distribution was proposed in [20], while a bivariate generalization of the IKu distribution was studied in [34].…”