How to calculate 90% confidence interval

Hi,

I have a question on determine the value of 90% cofidence from a set of data. The question shown below.

Q.Assume ln(abc) is normally distributed and hence estimate the abc that will be exceeded for 0.1%.

What I have done:

abc = textread('abc.txt', '', 'headerlines', 1);

Inabc=log(abc);

pd = fitdist(abc,'Normal')

pd =

NormalDistribution

Normal distribution

mu = -0.456292 [-0.554295, -0.358289]

sigma = 0.668189 [0.605717, 0.745143]

I have generate a normal distrubution by In(abc) but how to estimate the abc that will be exceeded for 0.1% .

Answer 1

[Star Strider]

Use the paramci funciton:

abc = readmatrix('abc.txt');
Inabc=log(abc);
pd = fitdist(abc,'Normal')
ci10 = paramci(pd, 'Alpha',0.1).'                   % 10% CI
ci05 = paramci(pd, 'Alpha',0.05).'                  % 5% CI

producing:

pd = 

  NormalDistribution

  Normal distribution
       mu = 0.792155   [0.703932, 0.880378]
    sigma =  0.60151   [0.545272, 0.670785]


ci10 =
    0.7182    0.8661
    0.5539    0.6590


ci05 =
    0.7039    0.8804
    0.5453    0.6708

I calculated the 5% CI simply to be certain I was reading them correctly. The transpose operation (.') puts them in row-order form to match the original fitdist output.

EDIT — (5 Oct 2020 at 12:08)

I copied your code as you posted it, then noticed that you are actually fitting ‘Inabc’, not ‘abc’.

The correct paramterrs for the transformed data are:

ci10 =
   -0.5384   -0.3742
    0.6153    0.7320

ci05 =
   -0.5543   -0.3583
    0.6057    0.7451

You could also have used:

    pd = fitdist(abc,'Lognormal')

producing the same results.

.