How do I construct a joint pdf for a uniformly distributed sample that is drawn without replacement?

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Kenneth Carling

I do not think your question is entirely clear. If you know the distribution to be U(a,b) and you are sampling from this distribution, what is then meant by sampling without replacement? Do you mean you have a sample that is approximately uniform from which you are drawing subsamples (w/o replacement)?

Edward Fernando Toro Perea

The question lacks information, I think that you're talking about a simple random sampling without replacement, if so, you must meet the following requirements:

1. The sampling shape must have a sampling frame that specifies how to identify each unit in the population.

2. Also not known a priori on the possible values of Yi and other measurements associated with Yi.

3. In this case each unit is drawn with equal probability, in stages, without replacement, to have the n sample units.

For more information of the theme, you search the following words : "SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT".

Dr. Senthilvel Vasudevan

HI,

In sampling without replacement, the two sample values aren't independent. Practically, this means that what we got on the for the first one affects what we can get for the second one. Mathematically, this means that the covariance between the two isn't zero. In particular, if we have a SRS (simple random sample) without replacement, from a population with variance.

Guobing Lu

I agree with Kenneth Carling. Here just add a point:

Usually in statistics, the term "without replacement" is used for the situation of sampling from a finite population. For a continuous population, if you believe that the draws are correlated, to find the sample pdf, you may first investigate HOW a draw depends on the previous one, and then use the method of conditional distribution to construct the joint distribution.