Question

Why do we have different data models like Uniform, Geometric, Binomial, Poisson, and Normal? Can we apply the data model equations to any data set?

Answer 1

Ans:

We can't apply any data model equations to any data set,there are certain conditions to be satisfied to use any model,which are given below:

Binomial distribution:

There is a set of assumptions which, if valid, would lead to a binomial distribution. These are:

• A set of n experiments or trials are conducted.

• Each trial could result in either a success or a failure.

• The probability p of success is the same for all trials.

• The outcomes of different trials are independent.

• We are interested in the total number of successes in these n trials.

Poisson distribution:

The number of events that occur in any time interval is independent of the number of events in any other disjoint interval. Here, “time interval” is the standard example of an “exposure variable” and other interpretations are possible. Example: Error rate per page in a book.

• The distribution of number of events in an interval is the same for all intervals of the same size.

• For a “small” time interval, the probability of observing an event is proportional to the length of the interval. The proportionality constant corresponds to the “rate” at which events occur.

• The probability of observing two or more events in an interval approaches zero as the interval becomes smaller.

Geometric distribution:

The geometric distribution is an appropriate model if the following assumptions are true.

• The phenomenon being modelled is a sequence of independent trials.
• There are only two possible outcomes for each trial, often designated success or failure.
• The probability of success, p, is the same for every trial.

The above three data models Binomial,Poisson and geometric distribution are discrete data distribution models.

Similarly,Normal distribution is used for Continous data.

Normal distribition and uniform distribution are used for continuous data distribution models.