Finding the Distribution Parameters

This is a brief description on one way to determine the distribution of given data. There are several ways to accomplish this in R especially if one is trying to determine if the data comes from a normal distribution. Rather than focusing on hypothesis testing and determining if a distribution is actually the said distribution this example shows one simple approach to determine the parameters of a distribution. I’ve found this useful when I’m given a dataset and I need to generate more of the same type of data for testing and simulation purposes.

raw < - t( matrix(c(1, 0.4789,1, 0.1250,2, 0.7048,2, 0.2482,2, 1.1744,2, 0.2313,2, 0.3978,2, 0.1133,2, 0.1008,1, 0.7850,2, 0.3099,1, 2.1243,2, 0.3615,2, 0.2386,1, 0.0883), nrow=2) )( fit.distr <- fitdistr(raw[,2], "gamma") )qqplot(rgamma(nrow(raw),fit.distr$estimate[1], fit.distr$estimate[2]), (raw[,2]),xlab="Observed Data", ylab="Random Gamma")abline(0,1,col='red')simulated <- rgamma(1000, fit.distr$estimate[1], fit.distr$estimate[2])hist(simulated, main=paste("Histogram of Simulated Gamma using",round(fit.distr$estimate[1],3),"and",round(fit.distr$estimate[2],3)),col=8, xlab="Random Gamma Distribution Value")( fit.distr <- fitdistr(raw[,2], "normal") )qqplot(rnorm(nrow(raw),fit.distr$estimate[1], fit.distr$estimate[2]), (raw[,2]))abline(0,1,col='red')( fit.distr <- fitdistr(raw[,2], "lognormal") )qqplot(rlnorm(nrow(raw),fit.distr$estimate, fit.distr$sd), (raw[,2]))abline(0,1,col='red')( fit.distr <- fitdistr(raw[,2], "exponential") )qqplot(rexp(nrow(raw),fit.distr$estimate), (raw[,2]))abline(0,1,col='red')