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

Q(a,b)=bxexp(x2+a22)I0(ax)dx

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

Q(a,b)=1am1bxmexp(x2+a22)Im1(ax)dx

where a and b are nonnegative real numbers, and m is a positive integer. In this expression, Im-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.

Examples

expand all

Generate and Plot Marcum Q Function Data

This example shows how to use the marcumq function.

Create an input vector, x.

x = (0:0.1:10)';

Generate two output vectors for a=0 and a=2.

Q1 = marcumq(0,x);
Q2 = marcumq(2,x);

Plot the resultant Marcum Q functions.

plot(x,[Q1 Q2])

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.

See Also

Was this topic helpful?