Q: Interval estimation of the parameters of poisson distribution?

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The normal distribution is a continuous probability distribution that describes the distribution of real-valued random variables that are distributed around some mean value.The Poisson distribution is a discrete probability distribution that describes the distribution of the number of events that occur within repeated fixed time intervals, where the mean frequency is a known value, and each interval is independent of the prior interval(s)/event(s).

For the binomial, it is independent trials and a constant probability of success in each trial.For the Poisson, it is that the probability of an event occurring in an interval (time or space) being constant and independent.

Yes.

Why belong exponential family for poisson distribution

A poisson process is a non-deterministic process where events occur continuously and independently of each other. An example of a poisson process is the radioactive decay of radionuclides. A poisson distribution is a discrete probability distribution that represents the probability of events (having a poisson process) occurring in a certain period of time.

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Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution. Binomial is the most preliminary distribution to encounter probability and statistical problems. On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.

The Poisson distribution. The Poisson distribution. The Poisson distribution. The Poisson distribution.

The normal distribution is a continuous probability distribution that describes the distribution of real-valued random variables that are distributed around some mean value.The Poisson distribution is a discrete probability distribution that describes the distribution of the number of events that occur within repeated fixed time intervals, where the mean frequency is a known value, and each interval is independent of the prior interval(s)/event(s).

Independent events with a constant probability of occurrence over a fixed interval of time (or space).

The Poisson distribution may be used when studying the number of events that occur in a given interval of time (or space). These events must occur at a constant rate, be independent of the time since the previous occurrence.

For the binomial, it is independent trials and a constant probability of success in each trial.For the Poisson, it is that the probability of an event occurring in an interval (time or space) being constant and independent.

The Poisson distribution is discrete.

Yes.

J. E. Ehrenberg has written: 'Estimation of the intensity of a filtered poisson process and its application to acoustic assessment of marine organisms' -- subject(s): Poisson distribution, Underwater acoustics

Why belong exponential family for poisson distribution

The Poisson distribution is a limiting case of the binomial distribution when the number of trials is very large and the probability of success is very small. The Poisson distribution is used to model the number of occurrences of rare events in a fixed interval of time or space, while the binomial distribution is used to model the number of successful outcomes in a fixed number of trials.

I have no idea what you mean by inducing a distribution.If you assume that the number of events - people joining the queue - in a given time interval has a constant average rate and the the events are independent of one another, then arrivals in the queue follow a Poisson distribution.