By DArcy Wentworth Thompson
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Extra info for On Growth and Form: The Complete Revised Edition
Example text
N and j = 1, 2, . . , n to get an independent sample of size n 2 , namely [(X [i]( j) , Y(i)[ j] ), i = 1, 2, . . , n and j = 1, 2, . . , n]. For large k and under reasonable conditions (Gelfand and Smith 1990), the final observation in Eq. 5). Using the properties of SRSIS, [(X [i]( j) , Y(i)[ j] ), i = 1, 2, . . , n and j = 1, 2, . . , n], will produce unbiased estimators for the marginal means and distribution functions. Alternatively, we can generate one long standard Gibbs sequence and use a systematic sampling technique to extract every rth observation using a similar method as described above.
N and j = 1, 2, . . , n] should have a bivariate probability density function given by f ( j),(i) (u, v) = n! (n − i)! n! (n − j)! [1 − u]n− j f (u, v). 1) when k = 2. M. Samawi Moreover, to further improve some of the Monte-Carlo methods of integration, Al-Saleh and Samawi (2000) used steady-state ranked set simulated sampling (SRSIS) as introduced by Al-Saleh and Al-Omari (1999). SRSIS has been shown to be simpler and more efficient than Samawi’s (1999) method. In Samawi and Vogel (2013) work, the SRSIS algorithm introduced by Al-Saleh and Samawi (2000) was extended to multivariate case for the approximation of multiple integrals using Monte-Carlo methods.
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