Lognormal distribution between a specific range

Hello, I am trying to create a lognormal distribution using the 'lognrnd' command between 3000 and 10000

I want the distribution to be skewed to the right as that is the characteristic of lognormal distributions.

I attempted several times to create the distribution using the mean and the standard deviation of the associated normal distribution spread between 3000 &10000 but when I plot the histogram of the generated lognormal distribution, the distribution still looks like a normal distribution without skewness.

Any help is appreciated.

thanks

[the cyclist]

It would be helpful if you posted your code.

Answer 1

[the cyclist]

Here is some code that does roughly what you asked for.

r = lognrnd(8.6,0.2,100000,1);
figure
histfit(r);
skewness(r)

The red curve is the normal curve fit to the randomly generated data. The skew is evident, with a skewness of about 0.6.

[Dennis]

Thanks much for your reply and it certainly looks skewed. May I ask one more question on how did you come with 8.6 and 0.2?. I used exactly the same code with different MU and SIGMA

8.7372(MU) and 0.0799(SIGMA). I arrived at these numbers by using:

MU = log(M^2 / sqrt(V+M^2))

SIGMA = sqrt(log(V/M^2 + 1))

for the M & V in above equation I used the mean and variance of related normal distribution

norm_dist = 625O + 500.*randn(100000,1)

mu = log(6250^2/sqrt(500^2 + 6251^2));

sigma = sqrt(log(500^2/6250^2 +1));

%(i get mu = 8.7373 &sigma = 0.0799)

I think I am somewhere going wrong in the MU and SIGMA calculation.

Please let me know how to calculate these two parameters for the lognormal distribution.

Thanks again...

[the cyclist]

I just used trial and error to find parameters for the lognormal that would have the properties you asked for (specifically, a range of roughly 3000 to 10000). It looks to me like you did the calculation of mu and sigma correctly, so I would turn your question around and ask, "Why did you think that 500 was the correct value for the standard deviation of the normal?" That value seems much too small to get what you want. It seems that it should be around 1200.

[ashok singh]

I have similar problem. in place of range 3000-10000, I have a specification of data that is shown as nominal value of 3000 with unilateral tolerance as +7000. This may be written as 3000(0/+7000). I am taking here M=3000; and V= (7000/3)^2 , while considering 3 sigma unilateral tolerance spread. I used above-mentioned equations thus I got MU=7.7698 and SIGMA=0.6878. I then used lognrnd command with 100000 random numbers and made histogram. The problem is my lognormal histogram starts from zero and extends beyond 10000. why does not it starts at my nominal value 3000 ? I want that my histogram should start from 3000.What should I do (Hope, you got the problem) pls help. Thanks.

[Jeff Miller]

1. In this group it is more usual to start a new question rather than adding a new questionas a comment on a previous question.

2. Cupid may be helpful to you. For example, the following code:

myDist = Lognormal(7,1);
myDist.EstPctile([3000 10000],[.001 .999]);
myDist.PlotDens;
xrand=myDist.Random(10000,1);
figure; histogram(xrand);

produces the two attached figures, and it sounds like these are pretty close to what you want.