Abstract
This paper introduces a new lifetime distribution by mixing the first two lower record values and various distributional properties are examined. Statistical inference on distribution parameters are discussed with five estimators. A Monte Carlo simulation study is carried out to evaluate the risk behavior of these estimators for different sample of sizes. The distribution modeling analysis is provided based on real data to demonstrate the fitting ability of the proposed model. In addition, a lifetime regression model is described by re-parameterization on the log lifetimes. The superiority of proposed regression model is revealed in well-known models.
Highlights
In two decades, many statistical distributions have been brought into the literature
The weighted least squares estimator (WLSE) and Anderson–Darling estimator (ADE) have similar mean squared errors (MSEs) for all sample of size and they are better than the others
The MSE of maximum likelihood estimate (MLE) tends to MSE of WLSEs and ADEs for large sample size
Summary
Many statistical distributions have been brought into the literature. Transmuted families are given based on order statistics. Tanış and Saraçoğlu [7] examined a special model based on Weibull distribution of record based transmuted family of distributions. In terms of both distributional properties and statistical inference, in parallel with the study of [6]. We obtained the transmuted version of the Fréchet distribution based on lower record values.
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