The Skewed-Laplace Distribution

The Truncated skewed-Laplace distribution (TSL) is a generalized model of an exponential distribution. The TSL distribution offers more flexible representation of the pattern of efficiency in the data. This model was first introduced by Aryal and Rao[4] .The skew Laplace distribution as a generalization of the Laplace law should be a natural choice in all real-worldcircumstances in which some skewness is present. Several asymmetric forms of the skewed Laplace distribution have acted in the literature with different formulations. This distribution was developed using the idea introduced by O’Hagan and studied by Azzalini[1].Inusah and Kozubowskiconsidered a discrete analogue of Laplace distribution. Kozubowski and Inusah [7] proposed a discrete

In high concentrations, it causes the constriction of blood vessels throughout the body and consequent rise of pressure. Vasopressin helps prevent the loss of water from the body by reducing urine output and helping the kidney reabsorbs water in the body. Vasopressin is secreted by the cells of the hypothalamus nuclei and stored in the posterior pituitary for release as necessary. It stimulates contraction of the muscular tissues of the capillaries and arterioles, raising the blood pressure, and increase peristalsis, exert some influence on the uterus, and influences resorption of water by the kidney tubules, resulting in concentration of urine. Its rate of secretion is regulated chiefly by the osmolarityof the plasma. Also prepared synthetically or obtained from the posterior pituitary of domestic animals, used as an antidiuretic called antidiuretic hormone (ADH). This paper will analyze the biological data for release of vasopressin and calculate the Fuzzy Truncated Skew Laplace distribution mean residual life timem(t) and Fuzzy hazard rate function of Truncated Skew Laplace distribution model h(t).

2.Fuzzy Truncated Skew Laplace distribution(FTSL)

A random variable X is said to have the skew symmetric distribution if its probability density functionis given by f(x)=2g(x)G(λx) Where, g(x) and G(x)

[8]ME.Smith, FW.Flynn ,“Distribution of Fos-like immunoreactivity within the rat brain following intraventricular injection of the selective NK3 receptor agonist senktide”, J Comp Neurol, 426,2000, (413– 428).
[9]SL.Bealer,FW.Flynn,“Centralneurokinin 3 receptors increase systemic oxytocin release: interaction with norepinephrine”,ExpNeurol 184,2003,(1027–1033).
[10]T.Eguchi,Y.Takano, T. Hatae, R.Saito,Y.Nakayama, Y.Shigeyoshi,H .Okamura, JE.Krause, H. Kamiya ,“Antidiuretic action of tachykinin NK-3 receptor in the rat paraventricular nucleus”, Brain Res 743,1996,(49 –55).
[11]Y.Nakajima, K.Tsuchida,M.Negishi,S.Nakanishi ,“Direct linkage of three tachykinin receptors to stimulation of both phosphatidylinositol hydrolysis and cyclic AMP cascades in transfected Chinese hamster ovary cells”, J BiolChem 267, ,1992,( 2437–2442).
[12]Y-Q. Ding, R.Shigemoto, M.Takada, H.Ohishi, S.Nakanishi, N.Mizuno, “Localization of the neuromedin K receptor (NK3) in the central nervous system of the rat”, J Comp Neurol 364,1996,(290