Log Logistic and Weibull distribution

1) How to decide when to use Log Logistic and Weibull distribution to solve problems and know how to work such problems?

2) What are the alternative continuous distributions for Log Logistic and Weibull distribution. Which means if I don't use Log Logistic and Weibull, which distributions can I use instead to solve the similar problems?

[Muthu Annamalai]

Dua, What do you want to use the probability distributions (pdf) for? Do you want to sample data according to the pdf, or calculate functions of RV, or run Monte Carlo models?

I suspect you could use any pdf resembling the two you mention, if they share a close enough mahalanobis distance http://en.wikipedia.org/wiki/Mahalanobis_distance

I would look at classic texts by Papoulis http://www.mhhe.com/engcs/electrical/papoulis/

[Dua]

TQ for your reply. I want to use the pdf to sample data according to the pdf and to calculate functions of RV. I have an additional question:

In Normal distribution, I know that the 2 parameters are mean and standard deviation and I know the concepts and applications of Normal distribution. However, in Log Logistic distribution, what do the 2 parameters of alpha (scale) and beta (shape) stand for? Similar questions go to Weibull distribution, what do the 2 parameters of lambda (scale) and kappa (shape) stand for? What are the values or range of values for these 4 parameters? Where can I find some simple examples and simple exercises to understand the concepts of these 2 distributions?