Another Derived Modification of the Geometric Weighted Weibull Distribution

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Abstract
The aim of this generalization is to introduce a new modified weighted Weibull distribution called geometric weighted Weibull that was derived from the concept of the weighted distribution to provide better flexibility extension and tractability of the mathematical concepts of the weighted Weibull distribution. The major statistical and mathematical concepts the researchers adopted were parameter estimation, goodness-of-fit test, hazard function, quantile, survival function, entropy, and order statistics. The method of maximum likelihood estimation was adopted to estimate the unknown four parameters of the Geometric weighted Weibull distribution. The Monte Carlo simulation method is discussed using the quantile function to examine the performance of the parameters. The processes were performed using R-Software. A new modification of the Geometric weighted Weibull distribution is derived, and its probability characteristics are obtained. The shapes of the probability density function and hazard rate functions are investigated. The geometric weighted Weibull model assumes superior performance among the compared distributions, as evidenced by the Kolmogorov-Smirnov statistics and Akaike Information Criteria values.

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