Classical and Bayesian estimation for the truncated inverse power Ailamujia distribution with applications
Ahmed Mohamed El Gazar,
Mohammed ElGarhy,
Beih S. El-Desouky
Abstract:In this study, we suggest the truncated version of the inverse power Ailamujia distribution, which is more flexible than other well-known distributions. Statistical properties of the new distribution are considered, such as moments, moment generating function, incomplete moments, quantile function, order statistics, and entropy. We discuss various methods of estimation, such as the method of maximum likelihood, methods of least squares and weighted least squares, the method of the maximum product of spacings, … Show more
In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.
In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.
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<p>Accurate parameter estimation of extreme wind speed distribution is of great importance for the safe utilization and assessment of wind resources. This paper emphatically establishes a novel grey generalized extreme value method for parameter estimation of annual wind speed extremum distribution (AWSED). Considering the uncertainty and frequency characteristics of the parent wind speed, the generalized extreme value distribution (GEVD) is selected as the probability distribution, and the Weibull distribution is utilized as the first-order accumulation generating operator. Then, the GEVD differential equation is derived, and it is transformed into the grey GEVD model using the differential information principle. The least squares method is used to estimate the grey GEVD model parameters, and then a novel estimation method is proposed through grey parameters. A hybrid particle swarm optimization algorithm is used to optimize distribution parameters. The novel method is stable under different sample sizes according to Monte Carlo comparison simulation results, and the suitability for the novel method is confirmed by instance analysis in Wujiaba, Yunnan Province. The new method performs with high accuracy in various indicators, the hypothesis test results are above 95%, and the statistical errors such as MAPE and Wasserstein distance yield the lowest, which are 3.33% and 0.2556, respectively.</p>
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