# R/exp.test.R In goft: Tests of Fit for some Probability Distributions

#### Documented in exp_test

```# Tests for exponentiality

exp_test <- function(x, method = "transf", N = 10^3){
DNAME <- deparse(substitute(x))
if (sum(is.na(x)) > 0) warning("NA values have been deleted")
x <- x[!is.na(x)]
if (!is.numeric(x) || length(x) <= 1) warning(paste(DNAME, "must be a numeric vector containing more than 1 observation"))
x <- as.vector(x)
samplerange <- max(x) - min(x)
if (samplerange == 0) stop("all observations are identical")
n <- length(x)   # adjusted sample size without NA values
if (min(x) < 0) stop("The dataset contains negative observations. \nAll data must be non-negative real numbers.")
if(any(c("ratio", "transf") == method) == FALSE) stop("Invalid method. \nValid methods are 'transf'  and 'ratio'. ")
alternative = paste(DNAME," does not follow an Exponential distribution.")
# Test based on a transformation to approximately uniform r.v.
if(method == "transf"){
stat <- function(x){
n <- length(x)
b.check  <-   cov(x, log(x))
u  <- exp(-x / b.check)
variance <- (1 + trigamma(1)) / 16 + 1 / 12 + (log(2) - 1) / 8
t  <- sqrt( n / variance ) * (mean(u) - 1 / 2)
return(t)
}
stat_c <- stat(x)
if (n >= 200){
p1 <- pnorm(stat_c)
p2 <- 1 - p1
p.value <- 2*min(p1, p2)
}
if( n < 200){
null.distr  <- replicate(N, stat(rexp(n, rate = 1 )))
p1          <- sum(null.distr < stat_c) / N
p2          <- 1 - p1
p.value     <- 2 * min(p1, p2)
}
results <- list(statistic = c("T" = stat_c), p.value = p.value, data.name = DNAME,
method = "Test for exponentiality based on a transformation to uniformity ")
}

# Cox-Oakes test (based on the ratio of two scale estimators).
if (method == "ratio"){
co_stat <- function(x){
m <- mean(x)
lo <- log(x / m)
l <- log(x)
v <- (n + (1/m) * sum(x * (lo)^2) - (sum(x * lo))^2 / (n * m^2))^(-1)
u <- n + sum(l) - sum(x * l) / m
obs_stat <- sqrt(v) * u
return(obs_stat)
}
stat_c <- co_stat(x)
p1 <- pnorm(stat_c)
p2 <- 1 - p1
p.value <- 2 * min(p1, p2)
results <- list(statistic = c("CO" = stat_c), p.value = p.value,
method = "Cox-Oakes test for exponentiality", data.name = DNAME)
}
class(results) <- "htest"
return(results)
}

```

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goft documentation built on May 2, 2019, 6:32 a.m.