Probability distribution relationships
AbstractIn this paper, we are interesting to show the most famous distributions and their relations to the other distributions in collected diagrams. Four diagrams are sketched as networks. The first one is concerned to the continuous distributions and their relations. The second one presents the discrete distributions. The third diagram is depicted the famous limiting distributions. Finally, the Balakrishnan skew-normal density and its relationship with the other distributions are shown in the fourth diagram.
A. AZZALINI (1985), A class of distributions with includes the normal ones, “Scandinavian journal of statistics”, 12, pp. 171-178.
E. L. CROW, K. SHIMIZU (1988), Lognormal distributions: Theory and Applications, Marcel Dekker, New York.
U. GATHER, U., KAMPUS, and N. SCHWEITZER (1998), Characterizations of distributions via identically distributed functions of order statistics, In: Balakrishnan, N., and Rao, C. ed., “Handbook of Statistics”, 16, Elsevier Science, pp. 257-290.
N. JOHNSON, S. KOTZ and N. BALAKRISHNAN (1994), Continuous univariate distributions, Vol. 1, 2nd ed. Wiley, New York.
N. JOHNSON, S. KOTZ and N. BALAKRISHNAN (1995), Continuous univariate distributions, Vol. 2, 2nd ed., Wiley, New York.
I. KOTLARSKI (1962), On group of n independent random variables whose product follows the beta distribution, “Collog. Math. IX Fasc.”, 2, pp. 325-332.
W. KRYSICKI (1999), On some new properties of the beta distribution, “Statistics & Probability Letters”, 42, pp. 131-137.
L. LEEMIS (1986), Relationships among common univariate distributions, “The American Statistician”, 40, pp. 143-146.
M. SHARAFI, J. BEHBOODIAN (2008), The Balakrishnan skew-normal density, “Statistical Papers”, 49, pp. 769-778.
J.W. RIDER (2004), Probability distribution relationships, http://www.jwrider.com.
H. A. TAHA (2003), Operations Research: An introduction, 3rd ed, Macmillan Publishing Co.