How to create a skewed distribution that is truncated?

Question

Jacob Elder 2019-10-15

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https://ww2.mathworks.cn/matlabcentral/answers/485537-how-to-create-a-skewed-distribution-that-is-truncated

回答： Adam Danz 2019-10-15

Hello,

I am trying to make a right skewed truncated distribution with a mean of 75 and SD of 15 that does not produce values outside of 0 and 100.

I understand that you can truncate a normale distribution probability object with... t = truncate(pd,lower,upper)

Meanwhile, I know that you can also create a skewed distribution with: pearsrnd(mean,sd,skew,kurt,trials,col)

However, I am not sure how you create both a skewed distribution and extract values from it that also is truncated? Can anyone assist me with this?

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Jacob Elder 2019-10-15

编辑：Jacob Elder 2019-10-15

That's a fair point and good recommendation. I did as you mentioned and it worked well.

mean = 75;
sd = 5;
skew = .3;
kurt = 2.7;
col = 1
trial = 1;
rating = [];
while length(rating)<100
r = pearsrnd(mean,sd,skew,kurt,trial,col);
if r > 0 & r < 100
rating = [rating ; r];
end
end
hist(rating)

With data as:

8622107925150
1555187688770
3512486969151
4146040772961
5851649991042
3599490492784
4590822947942
1753624683229
0157085567081
3164705444270
8591991541973
4617019190464
0304110319437
3634567624738
4805220787830
2771116347441
8479490651980
6408620461409
7497657770307

etc.

And plot as

I need to fiddle with the skew and kurtosis but your idea helped with my issue. Thanks!

Adam Danz 2019-10-15

Great! I'll copy my comment as an answer below so your question appears as solved. Note that this method biases the distribution which could result in distribution that doesn't maintain the properties of the actual desired distribution. But that's at least partial true of any bounded distribution.

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Answer 1

Adam Danz 2019-10-15

1
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/485537-how-to-create-a-skewed-distribution-that-is-truncated#answer_396521

(continuing from the comments under the question)

One solution is to just truncate the distribution yourself by producing the distribution, cutting out values beyond your bounds, and replacing them with a new draw of numbers from the same distribution. That process could be set up in a while-loop that ends when the number of accepted values reaches your specification. Note that this could bias your distribution as is discussed in the comments under the question.