DnE (version 1.0)

is.nbinom: is.nbinom

Description

judge if the data obey negative binomial distribution

Usage

is.nbinom(x, m, a, p0 = NULL, r0 = NULL)

Arguments

x

data

m

the numbers of intervals of data you wanna devide

a

confidence level

p0

the pobability that result is success in each experiment

r0

the number of successful events you want to wait for

Value

• if data obey the distribution, return a value represent the likelihood, the larger the better; else return -1.

Details

Given a set of observations from a certain distribution, this function is used to test whether the observations are from a distribution of Two negative binomial distribution distribution or not. The function will work better if the number you choose to devide the interval is between 5 and 20.

References

ROBERT V. HOGG/ALLEN T. CRAIG (Fifth Edition) Introduction Mathematical Statistics.

See Also

is.dt , DnE-package

Examples

require(stats)
examplecheck<-rnbinom(100,10,0.1)
is.nbinom(examplecheck,10,0.05)
#examplecheck is a dataset with a defined distribution you want to check. Suppose you want to devide the interval into 10 parts and want the confidence level to be 0.05#
##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (x, m, a, p0 = NULL, r0 = NULL) 
{
    re = 1
    for (i in 1:length(x)) if (x[i] <= 0) 
        re = -1
    p = rep(0, m + 2)
    y = rep(0, m + 2)
    q = 0
    if (re == -1) {
        return(-1)
    }
    else {
        x1 = mean(x)
        sum = 0
        for (i in 1:length(x)) {
            sum = sum + x[i]^2
        }
        x2 = sum/length(x)
        if (is.null(p0) && is.null(r0)) {
            p0 = x1/(x2 - x1^2)
            r0 = round(p0 * x1/(1 - p0))
            df = m - 1
        }
        else if (is.null(p0)) {
            p0 = 1 - x1^2/(x2 - x1^2)
            df = m
        }
        else if (is.null(r0)) {
            r0 = round(p0 * x1/(1 - p0))
            df = m
        }
        else {
            df = m + 1
        }
        if (p0 > 0 && p0 < 1 && r0 > 0) {
            di = max(x) - min(x)
            for (i in 1:m) {
                p[i] = pnbinom(min(x) + round(di * i/m), r0, 
                  p0) - pnbinom(min(x) + round(di * (i - 1)/m), 
                  r0, p0)
                if (p[i] == 0) {
                  break
                }
                for (j in 1:length(x)) if (x[j] > (min(x) + di * 
                  (i - 1)/m) && x[j] <= (min(x) + di * i/m)) 
                  y[i] = y[i] + 1
                q = q + (y[i] - (length(x) * p[i]))^2/(length(x) * 
                  p[i])
            }
            p[m + 1] = pnbinom(Inf, r0, p0) - pnbinom(max(x), 
                r0, p0)
            q = q + (y[m + 1] - (length(x) * p[m + 1]))^2/(length(x) * 
                p[m + 1])
            p[m + 2] = pnbinom(min(x), r0, p0)
            y[m + 2] = length(which(x == min(x)))
            q = q + (y[m + 2] - (length(x) * p[m + 2]))^2/(length(x) * 
                p[m + 2])
            q0 = qchisq(1 - a, df)
            if (q <= q0) {
                return(q0 - q)
            }
            else {
                return(-1)
            }
        }
        else {
            return(-1)
        }
    }
  }