Analytical Solution of two Model Equations for the Variation of Capital Market Prices (Published)
This paper investigated different methods for estimation of parameters of Weibull distribution, using Mean Square Error (MSE) as a criterion for selecting the best model. The result showed that Method of Moments outstripped other methods. In the same vain, the estimated results were logically extended to form a matrix that would help in predicting different commodity price processes, and the result obtained by exploring the properties of the principal component analysis solution and results showed the level of proportion accounted by first Principal Component Analysis (PCA). However, the eigenvectors describe the direction of the stock market prices in terms of changes in short-run and long-run respectively.
Citation: Amadi, Innocent Uchenna, Uchechi, Ahana and Anyamele, Bethel Azunna (2022) Analytical Solution of two Model Equations for the Variation of Capital Market Prices, International Journal of Mathematics and Statistics Studies, Vol.10, No.3, pp.12-27
Keywords: principal component and matrix solution, stock market prices, weibull
On A Closed-Form Estimator of the Shape Parameter of the Three-Parameter Weibull Distribution (Published)
The shape parameter of the three-parameter Weibull distribution () was considered in this study. Known estimation methods like the maximum likelihood, method of moment and maximum product of spacing do not have closed-form estimators for the shape parameter of the three-parameter Weibull distribution rather they involve iterative procedures which may be time-consuming and are less tractable. Dubey (1967), Goda et al (2010) and Teimouri and Gupta (2013) have proposed closed-form estimators for . In this study, a closed-form estimator for is proposed and the proposed estimator is compared with the existing closed-form estimators proposed by the authors mentioned above. To compare the accuracy of the estimators, Monte Carlo simulation is performed. Simulated data from the Weibull distribution are used to check the accuracy of the estimators and the root mean square error (RMSE) is used as a metric for accuracy. The results show that in general, the proposed estimator performs better than the other three closed-form estimators that were compared.
Keywords: Accuracy, Estimators, Parameter, tractability, weibull