# Questions tagged [inverse-gaussian-distribution]

A right skew continuous probability distribution on positive real numbers.

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### Closed-Form Lambda for Yeo-Johnson-Transformed Normal-Inverse-Gaussian-Distributed Random Variables

I would like to know whether there exists a closed-form solution for the $\lambda$-parameter that maximizes the log-likelihood function of Yeo-Johnson transformed random variables that (before the ...
• 435
39 views

### How do I appropriately code a gamm() model with an inverse.gaussian family and autocorrelation structure?

I am incredibly new to generalized additive modeling, so I apologize in advance for any and all naiveté. But I believe GAMMs are the appropriate methodology for my data. I am working with fish ...
1 vote
63 views

### Properties of the inverse normal cdf and permutation probabilities as models for horse racing

Let $T_i$ be the running time of horse $i$ and $T_i \sim N(\theta_i,1)$ and the $T_i$'s are independent. Then Henery (1981) showed that the probability $P(T_1<T_2<\cdots <T_n)$ can be ...
22 views

### Adequate sample size for non-normal population

There are 197,058 record holders (population) with an average of K shares each. I don’t know K, and the sample collected so far of ~24,000 observations appear to be non-normal (inverse gauss). I’m ...
• 1
1 vote
420 views

### How to interpret beta coefficients of a generalized linear model using inverse gaussian

I made a generalized linear model with an inverse gaussian link. ...
• 11
58 views

### The mean of Gaussian distribution subject to another Gaussian distribution, how to derive it？

I got a fomula $$N(y;cx,R)N(x;\bar{x},\Sigma)=N(y;c\bar{x},S)N(x;g,F)$$ where: \begin{align}S&=c\Sigma c^T+R\\g &=\bar{x}+\Sigma c^Ts^{-1}(y-c\bar{x})\\F &= \Sigma - \Sigma c^T s^{-1} c \...
123 views

### The probability/cumulative density function for inequality of two random variables

I have two random variables X and Y which came from different inverse gaussian (IG) ...
• 718
125 views

### Relationship between standard normal distribution and normal distribution

Assume we have $X\sim \mathcal{N}(\mu,\sigma^2)$. What is the value/formula of $$\Phi^{-1}(\Phi_{\mu, \sigma}(x)),$$ for any $x\in \mathbb{R}$? $\Phi^{-1}$ denotes the inverse of the standard normal ...
400 views

### 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 ...
• 1,660
338 views

### 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 ...
1 vote
166 views

### I'm getting confused with Gaussian Process Prior sampling

I'm having a hard time understanding Gaussian Processes prior sampling. Here is the article from medium I'm using to learn about Gaussian Processes Article link. I'm going to start off by explaining ...
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1 vote