Affiliations: [a] Nilkamal School of Mathematics, Applied Statistics and Analytics, SVKM’s NMIMS Deemed to be University, Mumbai, India | [b] Department of Statistics, University of Mumbai, Mumbai, India
Correspondence:
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Corresponding author: Pradnya Khandeparkar, Nilkamal School of Mathematics, Applied Statistics and Analytics, SVKM’s NMIMS Deemed to be University, Mumbai, India. E-mail: [email protected].
Abstract: Laplace probability density function with additional shape parameter that regulates the degree of skewness is a skew Laplace distribution. The various forms of skew Laplace distribution are found in the literature, the distributions defined by Mc Gill (1962), Holla and Bhattacharya (1968), Lingappaiah (1988), Fernandez and Steel (1998). The skew log Laplace distribution is the probability distribution of a random variable whose logarithm follows a skew Laplace distribution. In this paper, the classical optimum tests for skewness parameter of skew log Laplace distribution (SLLD) derived from Lingappaiah (1988) distribution are discussed. Uniformly most powerful test, uniformly most powerful unbiased test and Wald’s sequential probability ratio test for skewness parameter are compared. The exact likelihood ratio test and Neyman structure test for testing skewness parameter when scale parameter is known are derived. Finally, the underreported income of Road Transport Company is analysed on the basis of the tests derived in this paper.
Keywords: Skew log Laplace distribution, uniformly most powerful test, uniformly most powerful unbiased test, sequential probability ratio test, likelihood ratio test, Neyman structure test
