Motivation for statistical distributions As statisticians, we come across many distributions under the banners "discrete" or "continuous", and "univariate" or "multivariate". But can anyone provide a good reason behind the existence and motivation for so many distributions? How do we get them? And what can a layman understand from it?
What is the logic behind the existence of distributions?
 A: In many cases a distribution can be described as a result of some idealized experiment. For example if we flip a fair coin $n$ times the number of heads will follow a binomial distribution with parameters $n$ and .5. These idealized experiments are often used as models; they are used as simplified representation of how the data came to be. There are obviously many such models, and as a consequence many distributions. If you want the logic behind all distributions, then that will require a book of many volumes, e.g.:
N. L. Johnson, S. Kotz and N. Balakrishnan (2000). Continuous Multivariate Distributions, Vol. 1 (second edition), New York: Wiley & Sons.
N. L. Johnson, S. Kotz and N. Balakrishnan (1997). Discrete Multivariate Distributions. New York: John Wiley & Sons.
N. L. Johnson, S. Kotz and N. Balakrishnan (1995). Continuous Univariate Distributions, Vol. 2 (second edition), New York: John Wiley & Sons.
N. L. Johnson, S. Kotz and N. Balakrishnan (1994). Continuous Univariate Distributions, Vol. 1 (second edition), New York: John Wiley & Sons.
N. L. Johnson, A. W. Kemp and S. Kotz (1992). Univariate Discrete Distributions (second edition), New York: John Wiley & Sons.
A shorter list of distributions that is more suitable/affordable for owning yourself is:
Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions. Wiley
