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Question 5 [Avec R Consider the dataset faithful_data.txt. It contains the times between eruptions for Old Faithful, a Geiser in Yellowstone national park (a). Plot a histogram of the dataset and describe it. (b). Fit a normal distribution. (c). Use a QQ-plot to check if your fitted model is appropriate

Use R to solve.

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Answer #1

(a).

install.packages("fitdistrplus")
library(fitdistrplus)
head(faithful)
duration=faithful$eruptions
hist(duration, right=FALSE, col=colors, main="Old Faithful Eruptions", xlab="Duration minutes")

Old Faithful Eruptions w 寸 2 4 Duration minutes

(b)

FIT <- fitdist(duration,"norm")
class(FIT)
summary(FIT)

Fitting of the distribution ' norm ' by maximum likelihood
Parameters :
estimate Std. Error
mean 3.487783 0.06907846
sd 1.139271 0.04884568
Loglikelihood: -421.417 AIC: 846.8341 BIC: 854.0457
Correlation matrix:
mean sd
mean 1.000000e+00 4.795005e-11
sd 4.795005e-11 1.000000e+00

A normal distribution is fitted with the given data

(c)

plot(FIT)

Empirical and theoretical denS Q-Q plot LO 0 1 23 5 6 7 Data Theoretical quantiles Empirical and theoretical CDFs P-P plot 寸 0寸 0.2 0.4 0.6 0.8 Data Theoretical probabilities

From the QQ-plot we see that the normal fitting of the data was inappropriate since the quantile plots of the data versus the fitted normal distribution make a curved line. If it was a somewhat straight line, our assumption of normal fitting would have been correct.

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