marcumq - Generalized Marcum Q function

Syntax

Q = marcumq(a,b) Q = marcumq(a,b,m)

Description

Q = marcumq(a,b) computes the Marcum Q function of a and b, defined by

where a and b are nonnegative real numbers. In this expression, I₀ is the modified Bessel function of the first kind of zero order.

Q = marcumq(a,b,m) computes the generalized Marcum Q, defined by

where a and b are nonnegative real numbers, and m is a positive integer. In this expression, I_m-1 is the modified Bessel function of the first kind of order m-1.

If any of the inputs is a scalar, it is expanded to the size of the other inputs.

References

[1] Cantrell, P. E., and A. K. Ojha, "Comparison of Generalized Q-Function Algorithms," IEEE Transactions on Information Theory, Vol. IT-33, July, 1987, pp. 591–596.

[2] Marcum, J. I., "A Statistical Theory of Target Detection by Pulsed Radar: Mathematical Appendix," RAND Corporation, Santa Monica, CA, Research Memorandum RM-753, July 1, 1948. Reprinted in IRE Transactions on Information Theory, Vol. IT-6, April, 1960, pp. 59–267.

[3] Shnidman, D. A., "The Calculation of the Probability of Detection and the Generalized Marcum Q-Function," IEEE Transactions on Information Theory, Vol. IT-35, March, 1989, pp. 389–400.