Authors

• Akin A. Olosunde ¹
• Ajibola Taiwo Soyinka ²

¹ Department of Mathematics‎, ‎Obafemi Awolowo University‎, ‎Ile-Ife‎, ‎Nigeria‎

² Department of Statistics‎, ‎Federal University of Agriculture‎, ‎Abeokuta‎, ‎Nigeria

Abstract

In point estimation of the value of a parameter, especially when the estimator under consideration has a probability density function, then the limit that the expected value of the estimator actually equaled the value of the parameter being estimated will tend towards zero for the estimator to be asymptotically unbiased. Hence, some interval about a point estimate needs to be included to accommodate for the region of an unbiased estimate. But in several occurrences when the random variable is not normally distributed as is common in practice; then the interval estimated for the location and scale parameters may be too wide to give the desired assurance. In this study, we have obtained some results on the confidence procedure for the location and scale parameters for symmetric and asymmetric exponential power distribution which is robust in the case of skewness or  cases alike: tail heavier; and or thinner than the normal distribution using pivotal quantities approach, and on the basis of a random sample of fixed size $n$. Some simulation studies and applications are also examined.

Keywords

• Shape parameter‎
• ‎Short tails‎
• ‎exponential power distribution‎
• ‎confidence interval