Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

Fitness of Four-Parameter Beta Distribution Function for Forecasting Gold Reserve and Its Production Lifespan in Ghana

Ghana, renowned for its abundant gold reserves, plays a significant role in the global mining industry. Effective management and accurate forecasting of these reserves are vital for sustainable resource utilization and economic planning. Forecasting gold reserves and estimating their production lifespan are complex tasks that require robust statistical models capable of capturing the underlying dynamics of gold deposit accumulation and extraction. To this end, the four-parameter Beta distribution function emerges as a promising candidate due to its flexibility and ability to handle non-negative data. This research aims to investigate the fitness and applicability of the four-parameter Beta distribution function for forecasting Ghana’s gold reserves and estimating the production lifespan of this precious resource. The empirical paper relied mainly on quarterly secondary datasets on gold reserve between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Beta, Weibull, Normal, Logistic and Gamma were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the four-parameter Beta distribution provided the best fit for gold reserve in Ghana. At a 99.9% confidence level and considering the current annual average gold production estimate of 3,700,031.248 to 4,302,647.888 ounces, the projected lifespan of gold production in Ghana extends to the year 1,953,765. This astounding estimate suggests that the country’s gold reserves are expected to sustain production for an extended period, providing a critical resource for economic development and supporting the mining industry well into the distant future.

Reliability Estimation of Aviation Pyrotechnics System Based on Mixed Beta Distribution

For evaluating reliability of an aviation pyrotechnics system,a Bayesian reliability estimation method utilizing reliability information of a system and its units was put forward. Firstly,an inheritance factor was determined by chi-square goodness of fit test.Then the mixed prior distribution was obtained based on the inheritance factor. Finally, the density function of posterior distribution was obtained and used to assess the reliability of system.According to the new method, the reliability of an aviation pyrotechnics system was evaluated to reach 0. 989 6 at the confidence level of 0. 90. To reach the reliability index,the required numbers of trials of system and its units were given. It is instructional to apply the new method on the reliability estimation of aviation pyrotechnics systems.

Robust Optimal Operation of Active Distribution Network Based on Minimum Confidence Interval of Distributed Energy Beta Distribution

With the gradual increase of distributed energy penetration,the traditional optimization model of distribution network can no longer guarantee the stable and efficient operation of the distribution network.In order to deal with the inevitable uncertainty of distributed energy,a new robust optimal operation method is proposed for active distribution network(ADN)based on the minimum confidence interval of distributed energy Beta distribution in this paper.First,an ADN model is established with second-order cone to include the energy storage device,capacitor bank,static var compensator,on-load tap changer,wind turbine and photovoltaic.Then,the historical data of related distributed energy are analyzed and described by the probability density function,and the minimum confidence interval is obtained by interval searching.Furthermore,via taking this minimum confidence interval as the uncertain interval,a less conservative two-stage robust optimization model is established and solved for ADN.The simulation results for the IEEE33-bus distribution network have verified that the proposed method can realize a more stable and efficient operation of the distribution network compared with the traditional robust optimization method.

Bivariate Beta–Inverse Weibull Distribution:Theory and Applications

Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.

Return direction forecasting:a conditional autoregressive shape model with beta density

This paper derives a new decomposition of stock returns using price extremes and proposes a conditional autoregressive shape(CARS)model with beta density to predict the direction of stock returns.The CARS model is continuously valued,which makes it different from binary classification models.An empirical study is performed on the US stock market,and the results show that the predicting power of the CARS model is not only statistically significant but also economically valuable.We also compare the CARS model with the probit model,and the results demonstrate that the proposed CARS model outperforms the probit model for return direction forecasting.The CARS model provides a new framework for return direction forecasting.

ON SINGULAR MATRIX VARIATE BETA DISTRIBUTION

In this paper the density of the matrix variate beta distribution of rank lower than itsdimensionality is obtained with respect to a suitably defined differential form under the condi-tion that the difference between the identity and this matrix has full rank. As preliminaries,the Jacobian of a transformation related to decomposing a nonnegative-definite matrix into theproduct of a matrix of full column rank and its transpose and that of the transformation of anonnegative-definite matrix into its congruent matrix are established.

Negative Binomial Distribution Based Reputation Direct Update for Wireless Sensor Networks

In the reputation modeling of wireless sensor networks（WSNs） many literatures have proposed creative reputation indirect update methods,such as reputation integration,discounting,aging to eliminate,and filtering malicious reputation information. However,few have discussed the reputation direct update. In this paper,based on sound statistical theories,a negative binominal distribution method in the reputation direct update for WSNs is proposed. Results show that the proposed method is more suitable and time-saving for the reputation update of the resource constraint WSNs and can improve the computation power efficiency as well.

Cued search algorithm with uncertain detection performance for phased array radars

A cued search algorithm with uncertain detection performance is proposed for phased array radars. Firstly, a target search model based on the information gain criterion is presented with known detection performance, and the statistical characteristic of the detection probability is calculated by using the fluctuant model of the target radar cross section （RCS）. Secondly, when the detection probability is completely unknown, its probability density function is modeled with a beta distribution, and its posterior probability distribution with the radar observation is derived based on the Bayesian theory. Finally simulation results show that the cued search algorithm with a known RCS fluctuant model can achieve the best performance, and the algorithm with the detection probability modeled as a beta distribution is better than that with a random selected detection probability because the model parameters can be updated by the radar observation to approach to the real value of the detection probability.

A Formal Reputation System for Trusting Wireless Sensor Network

In this paper, a formal system is proposed based on beta reputation for the development of trustworthy wireless sensor networks （FRS-TWSN）. Following this approach, key concepts related to reputation are formal described step by step for wireless sensor networks where sensor nodes maintain reputation for other sensors and use it to evaluate their trustworthiness. By proving some properties of beta reputation system, the beta distribution is founded to fit well to describe reputation system. Also, a case system is developed within this framework for reputation representation, updates and integration. Simulation results show this scheme not only can keep stable reputation but also can prevent the system from some attacks as bad mouthing and reputation cheating.

Bayesian Assessment for Reliability of Binomial Components Based on Information Fusion of Similar Products

A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.

Designing Bayesian New Group Chain Sampling Plan For Quality Regions

Acceptance sampling is a well-established statistical technique in quality assurance.Acceptance sampling is used to decide,acceptance or rejection of a lot based on the inspection of its random sample.Experts concur that the Bayesian approach is the best approach to make a correct decision,when historical knowledge is available.This paper suggests a Bayesian new group chain sampling plan(BNGChSP)to estimate average probability of acceptance.Binomial distribution function is used to differentiate between defective and non-defective products.Beta distribution is considered as a suitable prior distribution.Derivation is completed for the estimation of the average proportion of defectives.This study includes four quality regions namely:(i)probabilistic quality region(PQR),(ii)quality decision region(QDR),(iii)limiting quality region(LQR),and(iv)indifference quality region(IQR).The estimated values for the BNGChSPare tabulated and the inflection point values are derived,based on different combinations of design parameters including both consumer’s and producer’s risks.For comparison with the existing plan,the operating characteristic curves expose that BNGChSP is a better substitute for industrial practitioners.

A Modified Epidemic Chain Binomial Model

Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infective from the same household with closed population. This paper emphasizes mainly on developing the probabilities of all possible epidemic chains with one introductory case for three, four and five member household. The key phenomenon towards developing this paper is to provide an alternative model of chain binomial model.

Quantitative spectrum occupancy evaluation in China: based on a large scale concurrent spectrum measurement

Due to the usable frequency becomes more and more crowed, dynamic spectrum access （DSA） is a new hope to solve this problem. However, DSA in China requires a quantitative analysis of the current spectrum utilization in frequency, temporal and spatial domains. In order to free the precious spectrum, spectrum regulation organizations must have a clear, detailed, up-to-date understanding of where, how and by whom spectrum is currently being used--such data is essential to sound policy decisions in the context of cognitive radio （CR）. In this paper, a concurrent spectrum occupancy measurement in south China was conducted to evaluate the practical spectrum occupancy with a digital wideband receiver covering from 20 MHz to 3 GHz. We also propose systemic spectrum measurement methodology, matrix format data storage, duty cycle （DC） evaluation metric and data mining process which can be a guideline for other researchers when they conduct the similar experiments. Quantitative analysis and characterization of the 4 different measurement locations are evaluated to promote the popularization of CR application in China. And a uniform Beta distribution channel occupancy model is also validated using real-scene measurement data. The experimental results demonstrate that there is a significant scope for license-exemption use of the released spectrum using CR technology.