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.
This paper uses the Kohonen Self-Organising Map (KSOM) to detect, diagnose, and classify induction motor faults. A series of simulations using models of the 3-phase induction motor based on real industrial motor parameters were performed using MATLAB/Simulink under fault conditions such as inter-turn, power frequency variation, over-voltage and unbalance in supply voltage. The model was trained using the input signals of the various fault conditions. Various faults from an unseen induction motor were fed to the model to test the model’s ability to detect and classify induction motor faults. The KSOM adapted to the conditions of the unseen motor, detected, diagnosed and classified these faults with an accuracy of 94.12%.
Sigmoid functions were used to approximate the cumulative gold production in Ghana. The functions examined were the logistic, Gompertz, Gaussian, Probit and the Hill, which were then used to predict into the future. Although all the five approximated models gave a good estimation of the reality, the Gompertz function was identified to give the best approximation of the observed trend of gold production in Ghana. The model was selected based on its high proportion of variance explained (R2 = 0.9402) as well as having the least value in terms of error (RMSE) and information loss (AIC). The model suggested that gold production could escalate to a level of 7040813 Oz in the future. It also showed that, industrial scale production of gold should be possible even after the year 2050 provided the current upward trend of gold production in Ghana continues. Keywords: Sigmoid, Logistic, Gompertz, Gaussian, Probit, Hill, Gold
The Artisanal and Small Scale Mining (ASSM) industry is of great importance to the Ghanaian economy. It provides employment for the teeming youth directly and indirectly and produces gold for the local goldsmiths, among other benefits. Concomitant to their operations, ASSM causes significant environmental pollution with chemicals, predominantly mercury. Mercury is used by small scale miners in the processing of ore mined because it is relatively easy to use and readily available. The laws regulating small scale gold mining in Ghana do not forbid the use of mercury even though there is a loud outcry against the use of mercury in small scale gold mining. The operations have resulted in the discharge of mercury into the environment indiscriminately. No attempt is made by the miners to recover lost mercury hence all of it is lost to the environment. This paper presents the findings of a study that investigated the trajectory of the mercury lost into the environment. The results showed that 2 g of mercury was lost to the environment for every gram of gold recovered through ASSM; 39% of it was lost to the atmosphere due to roasting of the amalgam whilst the remaining 61% was lost into water and spillage onto the ground. Keywords: Mercury, Atmosphere, Pollution, Environment, Socio-economic
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