Fitdist gives wrong answer

fitdist is givin me mu of 6.43686 with this code. Am i doing something wrong. I'm trying to get mu and sigma values to compare this data with log normal distribution

Add=16

Add = 16

%%info given in question 4
River_flood_level=[516 678 802 683 491 582 625 531 451 726 652 556 470 570 774 670 432 604 881 707 735 614 698 403 548 504 758 1000 419];
River_flood_level=River_flood_level+Add;
%%solution of question 4
fitdist(River_flood_level.','Lognormal')

ans = 
  LognormalDistribution

  Lognormal distribution
       mu = 6.43686   [6.35256, 6.52116]
    sigma = 0.22162   [0.175873, 0.29973]

[Paul]

Why do you think the result is incorrect? What are you expecting mu to be?

The fitted distribution looks pretty reasonable given the limited amount of data provided.

Add=16;
%%info given in question 4
River_flood_level=[516 678 802 683 491 582 625 531 451 726 652 556 470 570 774 670 432 604 881 707 735 614 698 403 548 504 758 1000 419];
River_flood_level=River_flood_level+Add;
%%solution of question 4
p = fitdist(River_flood_level.','Lognormal');
figure
histogram(River_flood_level,'Normalization','pdf')
hold on
plot(400:1200,pdf(p,400:1200))

Answer 1

[Star Strider]

The μ and σ values are in log units. Calculatee their exponentials —

Add=16

Add = 16

%%info given in question 4
River_flood_level=[516 678 802 683 491 582 625 531 451 726 652 556 470 570 774 670 432 604 881 707 735 614 698 403 548 504 758 1000 419];
River_flood_level=River_flood_level+Add;
%%solution of question 4
df = fitdist(River_flood_level.','Lognormal')

df = 
  LognormalDistribution

  Lognormal distribution
       mu = 6.43686   [6.35256, 6.52116]
    sigma = 0.22162   [0.175873, 0.29973]

Mean = exp(df.mu)

Mean = 624.4451

Sigma = exp(df.sigma)

Sigma = 1.2481

figure
hf = histfit(River_flood_level.', 10, 'Lognormal');
hold on
Line = findobj(hf,'Type','line');
ymu = interp1(Line.XData, Line.YData, exp(df.mu));
plot(exp(df.mu)*[1 1], [0 ymu], ':r', 'LineWidth',3)
hold off
Ax = gca;
Ax.XTickLabelRotation = 60;

.

[Emmeirrt]

Make sense, thank you!

[Star Strider]

As always, my pleasure!

I have not worked with lognormal distrbutions in a while (although all physiological parameters are lognormally distributed) so I had to rediscover that.

[Paul]

Mean is not the mean of the distribution and Sigma is not the sqrt of the variance of the distribution, so I'm still not sure what the OP is, or was, looking for. Perhaps @Emmeirrt can clarify.

[Star Strider]

Corrected —

Add=16

Add = 16

%%info given in question 4
River_flood_level=[516 678 802 683 491 582 625 531 451 726 652 556 470 570 774 670 432 604 881 707 735 614 698 403 548 504 758 1000 419];
River_flood_level=River_flood_level+Add;
%%solution of question 4
df = fitdist(River_flood_level.','Lognormal')

df = 
  LognormalDistribution

  Lognormal distribution
       mu = 6.43686   [6.35256, 6.52116]
    sigma = 0.22162   [0.175873, 0.29973]

m = exp(df.mu + df.sigma^2/2)

m = 639.9699

nu = exp(2*df.mu+df.sigma^2)*(exp(df.sigma^2)-1);

figure
hf = histfit(River_flood_level.', 10, 'Lognormal');
hold on
Line = findobj(hf,'Type','line');
ymu = interp1(Line.XData, Line.YData, m);
plot([1;1]*m, [0;1]*ymu, '--r', 'LineWidth',2)
hold off
Ax = gca;
Ax.XTickLabelRotation = 60;

.

[Emmeirrt]

Thank you! ı just needed the info that they are in lognormal. I fixed the rest myself. Sorry for not answering early

[Star Strider]

As always, my pleasure!

No worries!

Thank you for the follow-up (and for Accepting my Answer).