Assumption of normality in statistical analysis had been a common practice in many literature, but in the event where small sample is obtainable, then normality assumption will lead to erroneous conclusion in the statistical analysis. Taking a large sample had been a serious concern in practice due to various factors. In this paper, we further derived some inferential properties for log student’s t-distribution (simply log-t distribution) which makes it more suitable as substitute to log-normal when carrying out analysis on right-skewed small sample data. Mathematical and Statistical properties such as the moments, cumulative distribution function, survival function, hazard function and log-concavity are derived. We further extend the results to case of multivariate log-t distribution; we obtained the marginal and conditional distributions. The parameters estimation was done via maximum likelihood estimation method, consequently its best critical region and information matrix were derived in order to obtain the asymptotic confidence interval. The applications of log-t distribution and goodness-of-fit test was carried out on two dataset from literature to show when the model is most appropriate.
Transformer failure is a major problem confronting the Nigerian power sector, hindering the transmission and distribution of electric power to various households, institutions, and industries. Many of these transformer developed problem due to the old age of the transformers, overloading, in-availability of technical expertise, poor maintenance culture, manufacturer's faults, just to mention few. The present research focuses on providing half exponential power model for the failure of already installed transformers, with respect to years of installation up to the time of the first failure, using secondary data from the south western part of Nigeria as a case study. The results obtained showed that half exponential power performed better in modeling the first time failure of power transformers. This was possible because of the present of shape parameter which gives flexibility to half exponential power when compared with a half normal distribution.
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