In this paper, we introduce a new four-parameter mixture distribution called the Harmonic Mixture Burr XII distribution. The proposed model can be used to model data which exhibit bimodal shapes or are heavy-tailed. Specific properties like non-central and incomplete moments, quantile function, entropy, mean and median deviation, mean residual life, moment generating function, and stressstrength reliability are derived. Maximum likelihood estimation, ordinary least squares estimation, weighted least squares estimation, Cramér-von Mises estimation, and Anderson-Darling estimation methods were used to estimate the parameters of the distribution. Simulation studies was performed to assess the estimators and the maximum likelihood estimation was adjudged the best estimator. Using three sets of lifetime data, the empirical importance of the new distribution was determined. When compared to nine (9) extensions of the Burr XII distribution, it was clear that the proposed distribution fit the data better. Using the proposed model, a log-linear regression model called the log-harmonic mixture Burr XII is proposed.
In this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating function, and stress-strength reliability are presented. Estimators for the parameters of the harmonic mixture Fréchet distribution are derived using the estimation techniques such as the maximum-likelihood estimation, the ordinary least-squares estimation, the weighted least-squares estimation, the Cramér–von Mises estimation, and the Anderson–Darling estimation. A simulation study was conducted to assess the biases and mean square errors of the estimators. The new distribution was applied to three-lifetime datasets and compared with the classical Fréchet distribution and eight (8) other extensions of the Fréchet distribution.
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