cfail {ipsRdbs}

Weekly number of failures of a university computer system over a period of two years. This is a data vector containing 104 values.

Description

Weekly number of failures of a university computer system over a period of two years. This is a data vector containing 104 values.

Usage

cfail

Format

An object of class numeric of length 104.

Examples

 summary(cfail)
 # 95% Confidence interval 
 c(3.75-1.96 * 3.381/sqrt(104), 3.75+1.96*3.381/sqrt(104)) # =(3.10,4.40).
 x <- cfail 
 n <- length(x)
 h <- qnorm(0.975) 
 # 95% Confidence interval Using quadratic inversion 
 mean(x) + (h*h)/(2*n) + c(-1, 1) * h/sqrt(n) * sqrt(h*h/(4*n) + mean(x))
 # Modelling 
 # Observed frequencies 
 obs_freq <- as.vector(table(x))
 # Obtain unique x values 
 xuniques <- sort(unique(x))
 lam_hat <- mean(x)
 fit_freq <- n * dpois(xuniques, lambda=lam_hat)
 fit_freq <- round(fit_freq, 1)
 # Create a data frame for plotting 
 a <- data.frame(xuniques=xuniques, obs_freq = obs_freq, fit_freq=fit_freq)
 barplot(rbind(obs_freq, fit_freq), args.legend = list(x = "topright"), 
 xlab="No of weekly computer failures",  
 names.arg = xuniques,  beside=TRUE, col=c("darkblue","red"), 
 legend =c("Observed", "Fitted"), 
 main="Observed and Poisson distribution fitted frequencies 
 for the computer failure data: cfail")