Approximations, based on the application of ruin theory to pulse pileup, are presented for the evaluation of the incomplete gamma function Γ ( a , x ) for a >1 and x >; a ; these approximations become particul
It may be noted that (65) is an exact result and does not suffer from any approximation or series truncation as found in previous literature [9]. Unfortunately there are no known formulas to solve (65) in closed form. Nevertheless, the need of direct integration may be avoided by resorting...
(u) is the modified Bessel function of the second kind, see the appendix. Using (28), for large s we have the approximation p S(s) ≈ exp ` − √ 2 s /σ ´ √ 2σ `√ 2πσ s ´ d/2−1/2 , s 0, (8) ...
It is shown that by using elementary transformations, the Incomplete Beta Function can be turned into a form suggesting that a close approximation by a normal integral can be obtained. By using standard methods this approximation is then developed in the form of an asymptotic series consisting of...
To utilize traditional techniques to solve the optimization problem for the objective function (4), which becomes particularly challenging to evaluate analytically when dealing with multiple assets and exotic options with nonlinear payoffs, we employ a numerical approximation. As our integral is one dime...
Titterington (1984) proposed the same form of the equation as put forward here in terms of the IFS method, as an approximation to the EM algorithm. Lange (1995a) proposed the EM gradient method which con- verges exactly to Eq. (1) when the distribution belongs to an exponential family ...
where\({\mathcal{IG}}\)and\({\mathcal{N}}\)refer to the inverse gamma distribution and the multivariate Gaussian distribution, respectively. LetZ= [1,y,x2, …,xp], and letZcbe theNc× (p+ 1) submatrix ofZloaded with the complete cases only. Similarly, letx1,cbe the subvector of...
Therefore, special functions and approximation functions are often used to estimate them. In this particular study, new rational approximations for the Arrhenius and general temperature integrals were derived through the expansion of the incomplete gamma function. Two sets of these rational approximations,...
U. Blahak, Efficient approximation of the incomplete gamma function for use in cloud model applications, Geosci. Model Dev. 3 (2010) 329-336.Blahak U., 2010, Efficient approximation of the incomplete gamma function for use in cloud model applications, Geoscientific Model Development, 3, 329-...
APPROXIMATION(MATHEMATICSEXPONENTIAL FUNCTIONSCOMPUTER PROGRAMSCOMPUTATIONSFORTRANINTEGRATIONCOEFFICIENTSERROR ANALYSISANALYTIC FUNCTIONSCOMPLEX VARIABLESIn a previous report we studied rational approximations to the incomplete gamma function. These were based on the asymptotic expansion of the latter function. In the...