Towards Determining the Optimum Process Mean using an Exponential Distribution

Manufacturers are often faced with the problem of selecting the optimum process mean. Wen and Mergen (1999) used the unbalanced step loss function for measuring the cost of the non-conforming item and adopted a trade-off model for determining the optimum process mean. They assumed that the quality characteristic is normally distributed, the process variance constant and the process mean is unknown. This paper presents the modified Wen and Mergen model with a step loss function and piecewise function using an exponential distribution. The proposed model is a generalization of Wen and Mergens model. Keywords: step-loss function, piecewise linear loss function, exponential distributio

ICT and Market Efficiency: A Case Study of the Nairobi Securities Exchange

The efficiency of a capital market is important if savers funds are to be channeled to the highest valued stocks. A recent review of markets in Africa categorized the Nairobi Securities Exchange as one which has no tendency towards weak form efficiency. According to the random walk hypothesis stock market prices evolve in a random pattern and can therefore not be predicted. The weak form hypothesis examines whether or not security prices fully reflect historical returns. The NSE has increasingly used Information and Communication Technology (ICT) in their operation which has improved the integrity of the exchange trading systems and facilitated greater access to the securities market. ICT gives investors and market makers the opportunity to access current information so as to make informed decisions and may help make the market more efficient.  In an effort to establish efficiency of this market, we used non-parametric methods to establish the randomness of market returns at the NSE. The distribution of market returns appears normal although slightly negatively skewed and heavy tailed. The Q-Q and P-P plot also shows that the data approximates the normal distribution. The K-S and Runs test confirm that the data is not normally distributed which implies inefficiency in the weak form. This signifies market inefficiency of the weak form. Keywords:Random Walk, Market Efficiency, Weak form hypothesis, Frequency Tests, Runs test, Autocorrelation test, Kolmogorov-Smirnov tes

A Garch Approach to Measuring Efficiency: A Case Study of Nairobi Securities Exchange

The efficiency of capital markets is important if savers funds are to be channeled to the highest valued stocks. A recent review of markets in Africa categorized the Nairobi Securities Exchange as one which has no tendency towards weak form efficiency. Recent efforts to establish its efficiency have used mainly Ordinary Least Squares regression and have yielded inconclusive results. Ordinary Least Squares method assumes that the variance of the error term obtained is constant over time. However due to economic cycles some time periods are known to be generally riskier than others and the latter assumption fails to hold. There is therefore need to use other models which relax this assumption. The Autoregressive Conditionally Heteroscedastic models have been popular and widely used. They recognize that the value of the variance of errors depends upon previous lagged variances and lagged innovation terms. Kenya has also increasingly embraced ICT which may be attributed to the comparative lower cost of access to internet via computers and mobile phone technology. This is expected to increase the rational buyers in the market none of whom can influence prices in the market which may make the market more efficient. This study first used non parametric methods to check for randomness and independence of stock market returns at the Nairobi Securities Exchange. Results show that daily returns are non-random and the GARCH analysis shows that the current returns are dependent on the returns of the previous 3 days. The GARCH (3,1) model shows that returns on a particular day would be determined by the mean returns plus a white noise error term which would vary by 25.3% of return on day t-1, 9.5% of return on day t-2 and 12.05% of returns on day t-3 at 0.05 level of significance.  This signifies market inefficiency of the weak form. Keywords: Market Efficiency, Weak-Form Hypothesis, OLS, GARC