Pearson 5/Inverse Gamma/ Double Pareto My current research deals with landslide size frequency distribution which has been fit to a three-parameter inverse gamma function and a double Pareto function by previous researchers. I am trained as a civil engineer and can't make sense of how to build a program to fit my data in Fortran, MATLAB or R because I'm having some difficulty finding simplified explanations. I have so far been unable to find any books specifically on a 3-parameter inverse gamma relationship, only 1- and 2-parameter. 
Questions:


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*What textbooks would you suggest for a new reader in statistics?

*Is the Pearson V both the chi-squared AND the inverse gamma function?

*Can anyone assist me in understanding how to build these programs?

 A: These questions are on very different levels. Taking them in different order, 
Question 2. Chi-square is a Pearson III distribution and the inverse gamma a Pearson V distribution, so some confusion there. 
Three-parameter inverse gamma. The inverse gamma is usually cited in a two-parameter version. A three-parameter version that seems natural to your problem is in terms of value $-$ minimum value, i.e. a location parameter is added for some minimum size, which on physical grounds would usually be expected to be positive. Adding that third parameter makes the inverse gamma more difficult to fit, unless we are just ad hoc and use the observed minimum value. 
Double Pareto. I'm not clear exactly what distribution this is. The name of Pareto has been linked to so much, mostly stuff he never touched. Can you cite a formula? 
Practices with landslide data. I've found the small fraction [NB!] of the landslide literature I've sampled opaque on exactly how distributions were fitted and cavalier about whether it makes a difference how you do it. I've not noted, for example, much awareness of, or interest in, fitting by maximum likelihood. Frequently (pun intended) people bin the data and then fit density functions by some kind of least squares. 
Question 1. Textbook? A suitable book in this territory seems elusive. A good book would show SPICE: respecting the Science underlying different distributions, the Probability theory entailed, Inference procedures arising (e.g. hypothesis tests), the Computing (how to do it!) that is crucial, and exhibit Examples based on real data. Even the encyclopedic works of N.L. Johnson and S. Kotz, now passing to a younger generation of authors, notably N. Balakrishnan, is strong on P and I but misses out most of the S, C, and E. That may seem unfair and ungracious given the extraordinary effort that went into them, but there you go. 
Question 3. Code. I care very much how to program this, but that's off-topic here. 
Gratuitous extra. Some of the literature seems naive in seeking simple distributions for messy data (often landslide sets are highly heterogeneous e.g. in terms of mechanism). 
