Can be used to test whether the means of two normally distributed populations
are equal.
It is related to the incomplete beta integral:
1 - studentsDistribution(nu,t) = 0.5 * betaDistribution( nu/2, 1/2, z )
where
z = nu/(nu + t<sup>2</sup>).
For t < -1.6, this is the method of computation. For higher t,
a direct method is derived from integration by parts.
Since the function is symmetric about t=0, the area under the
right tail of the density is found by calling the function
with -t instead of t.
Student's t cumulative distribution function
Computes the integral from minus infinity to t of the Student t distribution with integer nu > 0 degrees of freedom:
$(GAMMA)( (nu+1)/2) / ( sqrt(nu π) $(GAMMA)(nu/2) ) * $(INTEGRATE -∞, t) (1+x2/nu)-(nu+1)/2 dx
Can be used to test whether the means of two normally distributed populations are equal.
It is related to the incomplete beta integral: 1 - studentsDistribution(nu,t) = 0.5 * betaDistribution( nu/2, 1/2, z ) where z = nu/(nu + t<sup>2</sup>).
For t < -1.6, this is the method of computation. For higher t, a direct method is derived from integration by parts. Since the function is symmetric about t=0, the area under the right tail of the density is found by calling the function with -t instead of t.