Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [inverse-gaussian-distribution]

A right skew continuous probability distribution on positive real numbers.

43 questions
18
votes
2 answers

Speed in m/s is normally distributed, but same data expressed as "Time for 10 meters" is not

I am trying to understand why the same data can be normally distributed if expressed in one way, but not normally distributed if expressed in another way. I have a variable that is "time taken to walk 10 meters" (in seconds). This data is not…
Tib
  • 183
  • 1
  • 6
14
votes
3 answers

Do test scores really follow a normal distribution?

I've been trying to learn which distributions to use in GLMs, and I'm a little fuzzled on when to use the normal distribution. In one part of my textbook, it says that a normal distribution could be good for modeling exam scores. In the next part,…
mistersunnyd
  • 595
  • 3
  • 13
6
votes
1 answer

Inverse Gaussian chi square connection

The inverse Gaussian distribution $IG(\mu,\lambda)$ is associated with the density $$f(x;\mu,\lambda) = \sqrt{\frac{\lambda}{2\pi x^3}}\,\exp\left\{-\frac{\lambda(x-\mu)^2}{2\mu^2x}\right\}\qquad \lambda,\mu,x>0$$ In Schuster (1968), the following…
Xi'an
  • 90,397
  • 9
  • 157
  • 575
4
votes
1 answer

How to get the prediction std using Gaussian Process in Scikit-Learn

I'm fitting some data using Gaussian Process (GP) in Scikit-Learn. As I understand, the GP requires to scale both X (input features) and Y (outputs) to standard normal distribution (mean = 0 and std = 1). I usually use the following code to scale my…
Rocco
  • 271
  • 2
  • 7
4
votes
0 answers

Expectation of log(1/X) when X follows inverse gaussian distribution

Can anybody help me in this question? How to derive the expectation of log(1/X) when X follows inverse Gaussian distribution? Found out a type of approximation for $\mathbb{E}[\log(X)]$ while $X \sim \mathcal{N}(\mu,\sigma^2)$ in this link (Expected…
Sandipan Karmakar
  • 536
  • 2
  • 10
3
votes
1 answer

Generalized mixed-effect regression model (GLMM) with negative reaction times as a result of baseline RT subtraction

I am hoping to get some advice for examining differences in reaction times (repeated sampling) as a measure of cognitive load between groups. Dataset: The response variable I am using is reaction times in ms relative to the mean(baseline RT)…
user1487545
  • 31
  • 2
3
votes
1 answer

How to choose a prior : family for a response with negative values?

I’m modeling percentage change in oxygen levels in the blood from a particular experiment. So my prior before seeing the data was an inverse gaussian distribution. But my data (response variable ) has some negative values. The family( ):…
amarykya_ishtmella
  • 373
  • 2
  • 7
3
votes
0 answers

P-values and confidence intervals for Inverse Gaussian GLMM?

I want to test the effects of different variables on Reaction Times data. Following the recommendations of Lo & Andrews (2015) I compared the AIC/BIC of three GLMM with a Gaussian, a Gamma and an Inverse Gaussian distribution with an identity link…
I.Nuel
  • 31
  • 1
3
votes
0 answers

Inverse Gaussian Distribution and the Central Limit Theorem

Let the random variables $Y_1,\ldots,Y_n$ be independent and identically distributed (i.i.d.) (standard) Inverse Gaussian random variables with parameters $\mu$ and $\lambda$. Then, let the random variables $\tilde{A}$ and $A$ be given, which are…
Anna
  • 213
  • 2
  • 5
3
votes
1 answer

Deriving Inverse Gaussian as First Passage Time of Wiener Process

Chhikara and Folks (1988) show that the inverse gaussian distribution arises as the first passage time for a wiener process. However, there are several steps I don't quite understand. In particular, some of the steps, e.g. the last one on p. 26, in…
Vegard Stikbakke
  • 489
  • 4
  • 8
3
votes
1 answer

How to apply glm(generalized linear model) in this simple example?

We are given 1) Y = $(Y_1,Y_2,...,Y_n)^T$ ~ Exponential 2) E[Y] = $\mu$ = X$\beta$, where X $\in R^{nxr}$ and $\beta \in R^r$ My question is can we apply the glm in this case? The case where the canonical link does not relate $\mu$ and $X\beta$.…
mathguy
  • 133
  • 5
3
votes
0 answers

Specifying distribution in generalized estimating equation GEE

GEE allows you to identify the distribution of the outcome variable and appropriate link function. How do you make this selection in a longitudinal model where the distribution changes in time. An extreme example would be number of drinking days in…
PTSDresearcher
  • 41
  • 4
2
votes
0 answers

Confused about inverse function (quantile function)

I read a post that says: "Math definition is that the quantile function is the inverse of the distribution function at α. It specifies the value of the random variable such that the probability of the variable being less than or equal to that value…
Maryam
  • 1,012
  • 1
  • 5
  • 20
2
votes
1 answer

Can't compute CDF for Inverse Gaussian distribution

I am trying to implement in Python the CDF of the Inverse Gaussian distribution: Inverse Gaussian pdf: $$ f(x) = \sqrt{\frac{\lambda}{2\pi x^3}}e^{-\frac{\lambda(x-\mu)^2}{2\mu^2x}} $$ Inverse Gaussian cdf: $$ F(x) =…
ИванКарамазов
  • 21
  • 3
2
votes
1 answer

Jacobian of Inverse Gaussian Transformation in Schwarz & Samanta (1991)

In the sample size $n=2$ case when transforming $\{x_1, x_2\}$ to $\{\bar{x}, s\}$ (where $X_1, X_2 \overset{iid}{\sim} IG(\mu, \lambda)$, $\bar{X}=\frac{\sum_i^2 X_i}{n}$, and $S=\sum_i^2 (\frac{1}{X_i}-\frac{1}{\bar{X}}$), Schwarz and Samanta…
mdawgig
  • 43
  • 6
1
2 3