Estimating arrival times of people in a shop using R. Part 4. Full article at: http://www.firsttimeprogrammer.blogspot.com/2015/07/estimating-arrival-times-of-people-in.html

arrivalTimes4.R

#-------------------------------------------------------------------------------
#                           Probability distributions
#-------------------------------------------------------------------------------

# Density plot
    #Since the rate is given as person/hour we need to set time in hours

            #Initial time  Final time       Step
            #0 hour        0.15 of an hour  0.001 of an hour
            #0 minutes     9 minutes        0.06 minutes = 3.6 seconds

# Time vector
time <- seq(0,0.15,0.001)

# 1 row, 2 columns
par(mfrow=c(1,2))

# Probability distribution plot
plot(time*60,dexp(time,rate=lambda),type='l',xlab='Minutes',
     ylab='Probability density',main='Probability distribution',col='blue',lwd=2)

# Cumulative distribution plot
plot(time*60,pexp(time,rate=lambda),type='l',xlab='Minutes',
     ylab='Cumulative probability',main='Cumulative distribution',col='red',lwd=2)

#-------------------------------------------------------------------------------
#                           Useful functions
#-------------------------------------------------------------------------------

# T = waiting time before an arrival (Random variable)
l = lambda

# Note: since it is more practical, t must be entered in seconds, 
# it will be converted into hours later

# Probability of waiting time of the arrival (T) being greater than t
# P(T > t)
p.right <- function(t)
{
    t <- t/60/60
    p <- exp(-l*t)
    return(p)
}

# Probability of waiting time of the arrival (T) being less than t
# P (T < t) cumulative dist
p.left <- function(t)
{
    t <- t/60/60
    p <- 1 - exp(-l*t)
    return(p)
}

print('Probability of waiting time before an arrival being greater than 3 minutes')
p.right(3*60)
print('Probability of waiting time before an arrival being less than 3 minutes')
p.left(3*60)