Re: Dynamical Systems and Expansion-Contraction

>>From Osher Doctorow

Well, the Marshall-Olkin bivariate exponential distribution turns out
to be the unique distribution with exponentially distributed marginals
which obeys the property:

1) P(X > x1 + x2, Y > y1 + y2, X > x1, Y > y1) = P(X > x1, Y > y1)P(X >
x2, y > y2)

for all nonnegative x1, x2, y1, y2. See Srikanth K. Iyer and D.
Manjunath and B. Manivasakan of (first two) Indian Institute of
Technology Kangur or Bombay and R. Manivasakan of Indian Institute of
Technology, Bombay, "Bivariate exponential distributions using linear
structures," in the marvellous Indian journal Sankya: The Indian
Journal of Statistics 2002, Volume 64, Series A, Pt 1, pp. 156-166,
which gives references for the Marshall and Olkin papers and other
recent applications of their own.

The "lack of memory property" (LMP) is sometimes used to refer to (1)
and its one-dimensional analogs or versions, but from the viewpoint of
PI, LMP is only the beginning of a marvellous exploration of memory
itself. Olkin is at Stanford and Marshall is/was at U. British
Columbia and U. Western Washington.

Osher Doctorow

.

Quantcast