Exponential distribution is a function of probability theory and statistics. This kind of distribution deals with continuous probability distributions and is part of the continuous analogue of the geometric distribution in math.
Why belong exponential family for poisson distribution
Exponential DistributionThe exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.
The exponential distribution and the Poisson distribution.
zero
The exponential distribution is a continuous probability distribution with probability density definded by: f(x) = ke-kx for x ≥ 0 and f(x) = 0 otherwise.
Why belong exponential family for poisson distribution
Exponential DistributionThe exponential distribution is a very commonly used distribution in reliability engineering. Due to its simplicity, it has been widely employed even in cases to which it does not apply. The exponential distribution is used to describe units that have a constant failure rate.
Poisson distribution or geometric distribution
The exponential distribution and the Poisson distribution.
zero
The exponential distribution is a continuous probability distribution with probability density definded by: f(x) = ke-kx for x ≥ 0 and f(x) = 0 otherwise.
Continuous
It is a continuous parametric distribution belonging to the family of exponential distributions. It is also symmetric.
The hypoexponential distribution is two or more exponential distribution convolved together, so:hypo[x] = integral of A*exp(-A*x)*B*exp(-B*(t-x)) from 0 to t.If you have more stages you do more convolutions.
the normal distribution is a bell shape and expeonential is rectangular
he uese it when he is lost like a hungry man
Poisson distribution shows the probability of a given number of events occurring in a fixed interval of time. Example; if average of 5 cars are passing through in 1 minute. probability of 4 cars passing can be calculated by using Poisson distribution. Exponential distribution shows the probability of waiting times between occurrences of events. If we use the same example; probability of a car coming in next 40 seconds can be calculated by using exponential distribution. -Poisson : probability of x times occurrence -Exponential : probability of waiting times between events.