Wrapped Length Biased Weighted Exponential Distribution
A new circular distribution to be called as wrapped length biased weighted exponential distribution with two parameters is proposed in this paper. The expressions for the characteristic function, the trigonometric moments and other related descriptive measures of the distribution are obtained. Estimation of the parameters is carried out using the maximum likelihood method and the estimators are shown to be consistent through a simulation study. The proposed model is fitted to a real-life data set on orientations and the goodness-of-fit of the distribution is assessed. The proposed distribution is found to be more appropriate in modelling the situations where the directions possessing lower magnitude have highest likelihood of occurrence and the likelihood of occurrence gradually decreases with an increase in magnitude of directions.