It has fewer parameters

It is a weighted mixture of exponentials with different rates

It is symmetric

The waiting time between two events

The number of rejections in a sampling process

The number of successes in a fixed number of trials

The number of trials until the first success

It guarantees 100% acceptance rate

It achieves high efficiency through precomputed regions

It doesn't require any uniform random numbers

The method becomes less statistically valid

The variance of the generated samples increases

The computation time decreases exponentially

The approximation to normality becomes better

A discrete approximation to a normal

The sum of several independent exponential random variables

The product of uniform random variables

The two expressions are mathematically identical

Both u and 1-u follow the same uniform distribution

Using u directly is computationally faster

The ln(1-u) formulation is mathematically invalid

The binomial CDF is difficult to invert analytically

The Mimicry Method always produces more accurate results

Mimicking the actual Bernoulli trial process is more intuitive

The Inverse Transformation Method cannot handle discrete distributions

It must be invertible

It must be symmetric

It must be differentiable

It must be bounded between 0 and 2

The acceptance rate decreases, making the method less efficient

The method becomes mathematically invalid

The method will only generate values from the tails of the distribution

The generated samples will have incorrect mean and variance

Multivariate normal distributions

Distributions that are explicitly defined as mixtures

Distributions with heavy tails

Distributions with simple inverse CDFs