First I am a new user of this site. Second my math background is very limited, although I do have a lot of experience in applied statistics.
Component or piece part failures on high value parts($1000 to $1,000,000 each).
Many of the theoretical statistical forecasting functions I use are based on the Poisson, exponential (single, double, and triple), moving average,weibull,and others.
Many actual failure distributions fit these theoretical distributions fairly well. Others don't.
Some have multiple series of zero failures per period, others don't. Many times the mean variance ratio is large i.e. the standard deviation is many multiples of the theoretical distribution mean.
I am looking for a practical tool or set of tools that can be used to derive functions from actual failure distributions if that is possible. Practical means fairly easy to program, preferably 1 or two parameter.
Any help is appreciated.