I am doing some analysis and I have come up with the following integral:
\int \frac{e^{-ax}}{1+be^{-cx}}dx
where a>0, b>0 and c>0.
I have found out this integral has a solution in terms of the Gaussian hypergeometric function http://en.wikipedia.org/wiki/Hypergeometric_function but it...
I'm afraid any attemp to obtain anything from the pdf/cdf analytically is a real nightmare as the resulting PDF is composed of four subequations, really huge... I spent one week computing these convolutions (yes, the involved variables are independent).
Basically, my random variable Y is Y = X...
No, the underlying distribution is much more complex. It is the result of the convolution of a generalized Pareto distribution with a uniform distribution, and with a uniform distribution again. The random variable is the sum of a generalized Pareto + uniform + uniform. I managed to obtain the...
Thanks! Unfortunately the underlying distribution in my problem isn't Gaussian. But I think I could use approximations to the mean of a function of a random variable: E[g(X)] \approx g(\mu) + \frac{1}{2}\sigma^2g''(\mu)
Hi All,
Is it possible to express the kurtosis \kappa, or the 4th central moment \mu_4, of a random variable X in terms of its mean \mu = E(X) and variance \sigma^2 = Var(X) only, without having to particularize to any distribution?
I mean, an expression like \kappa = f(\mu, \sigma^2) or \mu_4...
Thanks for quick reply.
Basically my problem is that I have a set of N "things" I observe at different time instants t, and I know the success/failure probabilities for each "thing". What I need is the probability to observe k successes in each observation of the N "things".
So I first...
Hi all!
I'm trying to solve the following problem.
The number of successes in a sequence of N yes/no experiments (i.e., N Bernoulli trials), each of which yields success with probability p, is given by the well-known binomial distribution. This is true if the success probability p is...
Hi guys,
thank you for your answers. I have found that if m<0 and n<0 then 1/(1 + exp(m*x + n)) can be expanded into Maclaurin series, which yields something like 1 + e^() - e^2*(). The terms can be multiplied by the numerator of the original integral, thus finally obtaining three integrals of...
Hi all,
I'm trying to solve the definite integral between 0 and inf of:
exp(a*x^2 + b*x + c)
--------------------- dx
1 + exp(m*x + n)
with a,b,c,m,n real numbers and a < 0 (negative number so it converges).
I've read in the forum's rules that I have to post the work that I have...