# Finding the Distribution Parameters

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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')

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