When we want to sample some specific distributions, we need to map through uniformly distributed sampling, because the pseudo-random numbers generated by computer algorithms are regarded as uniformly distributed.
Assuming that the uniformly distributed random variable is $ X $, the random variable of the specific distribution $ \ displaystyle p_Y (y) $ is $ Y = g (X) $. How to find this $ g (x) $ mapping?
Although this blog has some reference, I think this should be wrong. Because some examples are not satisfying, but I can map them by adding functions together. The following probability density mapping has been thinking for me for several hours, but the negative square root was not considered when it was originally squared.
For example, if I want to map $ X $ to $ \ displaystyle p_Y (y) = -2y + 2, y \ in [0,1] $, I can come up with the mapping $ Y = 1- \ sqrt {1-X}, X \ in [0,1] $.
For this simple distribution, I directly map it to an approximate highest order (here is $ X ^ 0.5 $), and then calculate the distribution function and then calculate the probability density to see how much is left, and then through the function of translation, symmetry Wait for the change to "make up".