# Infinite p-value when checking normality of distribution

My data has following distribution: I wish to determine if it is a Normal distribution, so:

> library(nortest)
Warning message:
package 'nortest' was built under R version 2.12.2
> sf.test(y)
Error in sf.test(y) : sample size must be between 5 and 5000
Anderson-Darling normality test
data:  y
A = 5487.108, p-value = Inf

> cvm.test(y)
Cramer-von Mises normality test
data:  y
W = 855.7627, p-value = Inf

> pearson.test(y)
Pearson chi-square normality test
data:  y
P = 2456556, p-value < 2.2e-16

> qqnorm(y); abline(0, 1)


When I do qqnorm, I found Can I conclude y does not have a normal distribution, since the p-value = INF and the qqnorm did not fit the abline?

Should I expect all these p-values close to zero or one when my distribution is in normal distribution? How about the pearson.test?

How should I interpret the numbers (A, W and P) before the p-values?

• It looks like your data is truncated at zero (i.e. no values below zero occur). That excludes it from coming from a normal distribution. – Nick Sabbe Jun 23 '11 at 9:54
• An infinite $p$-value seems to hint at some problem with the numerics. – cardinal Jun 23 '11 at 13:14

library(nortest)