What is difference between poisson and exponential distribution?
Answers
The Poisson distribution is a discrete one. This means that the outcome is a number. In traffic engineering, you can use the Poisson distribution to find the probability that a number of vehicle come to point within a certain period of time. For example you can select a 15-min interval and find the probability that zero, one, two, three, etc cars come during that period. On the other hand, the exponential distribution is a continuous one. This means that the outcome could be any real number. With a continuous distribution, you calculate the probability that a variable be smaller (or greater) than a given number or the probability that a variable be between two numbers (interval). The probability that the variable equal a number is zero with a continuous distribution. In traffic engineering, you can use the exponential distribution to find the probability that time headway be smaller (greater) than a number or between 2 numbers.
The negative exponential distribution can be derived from the Poisson count distribution. Consider the case when no vehicles arrive in a time interval, t , then the probability of zero vehicles arriving using the Poisson formula is P(0) = exp(-m) where m is the average number of vehicles arriving in the time interval t. P(0) means that the headway, h, between vehicles is more than the interval t. P(0) = P(h>t) = exp(-m) = exp(-V*t/3600). where V is the hourly flow rate.