# Recent content by fchopin

1. ### Integral with exponential terms?

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...
2. ### Kurtosis/4th central moment in terms of mean and variance

P.S.: The relation is \mu_4(Y) = \mu_4(X) + \mu_4(C) + 6Var(X)Var(C)
3. ### Kurtosis/4th central moment in terms of mean and variance

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...
4. ### Kurtosis/4th central moment in terms of mean and variance

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...
5. ### Kurtosis/4th central moment in terms of mean and variance

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)
6. ### Kurtosis/4th central moment in terms of mean and variance

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...
7. ### Simulation of beta-binomial distribution

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...
8. ### Simulation of beta-binomial distribution

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...
9. ### Integral of this exponential function: does it have a solution?

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...
10. ### Integral of this exponential function: does it have a solution?

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...