In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

The effects of the violations of normality and homogeneity of variances assumptions on the power of the one-way ANOVA F-test is studied in this paper. Simulation experiments were conducted to compare the power of the parametric F-test with the non-parametric Kruskal‒Wallis (KW) test in normal/non-normal, equal/unequal variances scenarios and equal/unequal sample group means. Each of these 184 simulation experiments was replicated N = 1000 times and power obtained for both F and KW tests. The Shapiro‒Wilk's test for normality and Bartlett's/Levene's tests for homogeneity of variances was conducted in each experiment. Results show that the power of the KW tests outperformed those of the F-tests in the 92 (85/92) non-normal cases. Although the power of the F-tests is higher than those of the KW tests in 85 out of the 92 experiments under normality assumptions, these differences, in all cases in this study are not significant (p > 0.05) using both t and sign tests. Based on these results, this study favours the KW test as a more robust test and safer to use rather than the F-test especially when the distributional assumptions of data sets are in doubt.

No abstract

This paper evaluates the lognormality assumption in Black-Scholes call options model. The data for this study were obtained from Australian Clearing House of Australian Securities Exchange (ASX). The data consists of fifty (50) enlisted stocks in the clearing house as products of monthly market summary for long term options which consists of the period of January 3rd, 2017 to December, 31st 2019 when there are no significant structural changes among the products arranged in 25, 27, 28, 29 and 30 maturity days. The Jarque-Bera test was used to test for the normality of Black-Scholes call of different maturity days and we observed that the normality was rejected at (p < 0.05). Further, normality test was also carried when the Black-Scholes options were log transformed and the normality test was rejected at p < 0.05. From the results of this study, the assumption of lognormality in Black-Scholes Option pricing model was violated.

No abstract