why mvnpdf give probablity larger than 1
tennic tennic
I get probablity larger than 1 when using mvnpdf.
what is the problem.
Thanks
Jerry
Roger Stafford
Jerry, remember that the 'pd' in mvnpdf stands for "probability density", not probability. Density means probability per unit value of the random variable. That can easily exceed 1. What has to be true is that the integral of this density function taken with respect to this value must be exactly 1.
Roger Stafford
John D'Errico
>
> I get probablity larger than 1 when using mvnpdf.
>
> what is the problem.
There is no problem, except in your expectation that
mvnpdf actually returns a probability. It does not.
http://en.wikipedia.org/wiki/Probability_density_function
Distributions with small variances will have a pdf that
exceeds 1 in places.
John
tennic tennic
Thanks.
if we know a pdf function(e.g. normal distribution), and want to know the "probability" of a given value, say x=1, what will people usually do? can I transform the pdf to a standard normal distribution and get the approximation P(x=1)~~pdf(X=1)?
Jerry
Nasser Abbasi
>
>
> Thanks.
> if we know a pdf function(e.g. normal distribution), and want to know the
> "probability" of a given value, say x=1, what will people usually do? can
> I transform the pdf to a standard normal distribution and get the
> approximation P(x=1)~~pdf(X=1)?
>
> Jerry
Probability that x=1 is zero. Remember, this is a continuous pdf.
To find the probability that the output of a random event is within some
range, you integrate the pdf over this range.
--Nasser
John D'Errico
> Thanks.
> if we know a pdf function(e.g. normal distribution), and want to know the "probability" of a given value, say x=1, what will people usually do? can I transform the pdf to a standard normal distribution and get the approximation P(x=1)~~pdf(X=1)?
>
> Jerry
The "probability that a normal (continuous)
random variable is 1? That event has measure
zero.
John
Roger Stafford
> if we know a pdf function(e.g. normal distribution), and want to know the "probability" of a given value, say x=1, what will people usually do?
For continuous distributions like the normal distribution, the probability that a random variable be exactly equal to any given constant must be zero! It can only be non-zero for intervals of non-zero length. This is very different from the concept of probability density at a given value. The probability density can be non-zero, even greater than one, but the probability that the variable is exactly equal to that value must be zero.
This situation is of course very different from that of a discrete distribution such as the poisson distribution in which individual points are given positive probability values. In the case of the poisson, the random variable is restricted to the non-negative integers. In that case the intervals between the integers are not allowed for the variables and the sum of all probabilities of individual points can therefore be successfully made to add up to just one.
Roger Stafford
Louis
To my understanding nlogn can't be negative since -log(p(x|obj)) however due to the fact that 'cluster' evaluates p(x|obj) using mvnpdf(x,mu.obj,mu.Sigma), then p(x|obj) 'can' have a value > 1 as in the above discussion. Hence, my nlogn 'can' be negative :S
So what is wrong? is it wrong to use mvnpdf or nlogn can be negative?
Thank you
Louis
Louis
Steven_Lord
"Louis " <wlo...@ryerson.ca> wrote in message
news:ic3go1$f8h$1...@fred.mathworks.com...
A probability density function (PDF) can take on values greater than 1.
http://en.wikipedia.org/wiki/Probability_density_function
A cumulative distribution function (CDF) cannot.
http://en.wikipedia.org/wiki/Cumulative_distribution_function
As the name suggests, MVNPDF computes a PDF not a CDF.
--
Steve Lord
sl...@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com
Juanjo
I am using mvnpdf to estimate the probability that a certain point (point of interest) belongs or not to a distribution defined by a mean vector and covariance matrix previously calculated.
If I understood previous posts well, I can integrate the pdf along an interval defined around my point of interest and that operation would return me a probability, right? If I am correct, I guess that interval around my point of interest should be "small enough", but I have no idea about what is an accepted interval length for these situations.
Thanks for your help.
"Steven_Lord" <sl...@mathworks.com> wrote in message <ic3qir$8hr$1...@fred.mathworks.com>...
Steven_Lord
"Juanjo " <jja...@gmail.com> wrote in message
news:j1rv0p$mmb$1...@newscl01ah.mathworks.com...
> Hi all,
> I am using mvnpdf to estimate the probability that a certain point (point
> of interest) belongs or not to a distribution defined by a mean vector and
> covariance matrix previously calculated.
>
> If I understood previous posts well, I can integrate the pdf along an
> interval defined around my point of interest and that operation would
> return me a probability, right? If I am correct, I guess that interval
> around my point of interest should be "small enough", but I have no idea
> about what is an accepted interval length for these situations.
I don't think you want the _P_DF then; I think you want the _C_DF. Check the
Wikipedia entries to which I linked in my previous reply for a description
of the difference.