SOME CERTAIN EQUIVALENCE FUNCTIONS

REQUIRING SERIES EXPANSIONS

OR NUMERICAL INTEGRATION METHODS

BETA DISTRIBUTION

Use Series expansion for EXP(-x/t )

Reverse order of integration and summation

LOGNORMAL DISTRIBUTION

Use transformation of variable: y = (ln(x)-m )/s

Use numerical integration (trapezoidal increments)

Let integration interval approach 0 (half it each iteration)

WEIBULL DISTRIBUTION

Use integration by parts:

For distributions with finite support, limit term is zero and integral can be evaluated numerically.