This might be motivated by the problem at hand. For instance, in reliability, failure data may be measured as discrete variables, like the number of shocks or cycles. Assigning a non zero prob to the number of shocks between 3.6 and 3.8 should be odd !!

There can be different ways of discretizing a continuous distribution, though, depending on the property we want to preserve.

thank you Mr Moinak Bhaduri.

There is methods that allow you to avoid discretization e.g.:

https://www.researchgate.net/publication/223504164_Bayesian_classifiers_based_on_kernel_density_estimation_Flexible_classifiers?ev=prf_pub

However, discretization have advantages such as faster computation or more easy to show results to non-scientists:

https://www.researchgate.net/publication/215739042_Fish_recruitment_prediction_using_robust_supervised_classification_methods?ev=prf_pub

Article Bayesian classifiers based on kernel density estimation: Fle...

Article Fish recruitment prediction, using robust supervised classif...

We don't need to discretize. One can fit parametric models or smooth non-parametric curves if we need to using standard statistical principles e.g. maximum likelihood

Sometimes discretization of continuous random variables is very useful. An example is when you need to compute the distribution of a compound random variable. This is the case in actuarial science, where the aggregate claims are sum of individual claims, and the number of individual claims is itself a random variable. See for instance the book Loss Models, by Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot.

The following article can be very useful to answer you:

Chen, S., Pollino, C., 2012. Good practice in Bayesian network modelling. Environ.

Model. Softw. 37, 134e145.

This is an interesting question. For actuarial science and insurance, we also are sometimes interested in the opposite: continuitizing a discrete distribution. Such usually can be accomplished by introducing a so-called "jitters". Please refer to my paper with P. Shi on "Longitudinal Modeling of Insurance Claim Counts Using Jitters". Our purpose was mainly to be able to directly apply copulas to continuitized multivariate discrete random variables.

The discretization of continuous distributions has also been used in the actuarial literature. For example, in a life or mortality table, death rates are sometimes reported for age intervals.

I will side with Richard Gill. Don't do it, unless you really have to. This way you will certainly distort your real data. However:

- in physical sciences your "continuous" data are in fact discrete. This is because of finite resolution of independent variable, say temperature. Even the best temperature controler keeps it within some range. Even if you record the "momentarily values" of temperature, then you know it only up to the resolution of your thermometer (plus the inertia of a sensor ...). Of course, you can discretize such data using much wider "bins", but such a procedure will only work satisfactorily when the dependent variable in in fact temperature almost insensitive. Well, this example has (almost) no relation to probability distribution.

- in less precise sciences: we have to classify somehow things like "degree of angriness", say as "crazy", "extremely angry", "very angry", "angry", "moderately angry", "not angry at all". We simply don't know how to do better.

The unquestionable advantage of discretizing the probability distributions, those based on experimental data, is enormous economy of storage keeping such data.

There is also the question of how to discretize: how many bins? bins of equal or not equal width?, etc.

Thank you all i appreciate your help.:)

People discretise continuous variables to calculate aggregate distributions (FFT, Panjer, etc) as already mentioned.

Discretising can also be used when you want to build a decision or event tree with a chance node that is a continuous variable.

any software to discretize continuous probability distributions?