Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [logistic-distribution]

A symmetric distribution which CDF is the logistic function.

See https://en.wikipedia.org/wiki/Logistic_distribution

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Logistic Regression - Error Term and its Distribution

On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in accordance with the distribution of the response…
user61124
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Why is the logistic distribution called "logistic"?

What is "logistic" about the logistic distribution, in a common sense way? What is the etymology of and the lexical rationale for the name, not just pure math definition?
Multifix
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Multivariate logistic distribution

The normal distribution can be generalized into the multivariate normal distribution. Can the logistic distribution also be generalized into a similar multivariate distribution? Is there a multivariate generalization of the logistic distribution…
Angelorf
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How is Logistic Regression related to Logistic Distribution?

We all know that logistic regression is used to calculate probabilities through the logistic function. For a dependent categorical random variable $y$ and a set of $n$ predictors $\textbf{X} = [X_1 \quad X_2 \quad \dots \quad X_n]$ the probability…
Eduardo Vieira
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What is $\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$ for $c\in\mathbb{R}$

It is straightforward to show $$\int_{-\infty}^{\infty}\Phi(a+bx) \phi( x ) dx = \Phi\left(\frac{a}{\sqrt{1+b^2}}\right)$$ but what value does $$\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$$ have for $c<\infty$, e.g., for $c=0$? Even a good…
Jenny Reininger
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What is the probability distribution used in logistic regression called?

In logistic regression, we set the probability of predicting a target $y$ given a data $x$ as, $\Pr(Y = 1|X;w) = \dfrac{\exp(w^TX)}{(1+\exp(w^TX))}$ What is exactly this probability distribution (or more accurately, conditional probability mass…
Curaçao Hajek
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How to visualise coefficients of a Binomial Logistic Regression?

Hello all! Do you have an idea how best visualise the data from this table knowing they are coefficients of binomial logistic regressions? What I would like to visualise is a confrontation between the predictors likely to influence 'paying…
Mab
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Why does the glm function converge and not give an error when all y's are equal to the same value?

I need to fit a univariate logistic model with few observations (between 10 and 20). In some cases, y is equal to the same value (example 1) for all observations. Theoretically, the model should not converge. But, when I use the glm function in R it…
Ph.D.Student
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Regression with Logistic-Distribution errors (NOT Logistic Regression)

I was wondering if anyone ever tried to do a regression where the errors, instead of normal, would be assumed to be from the Logistic Distribution. I don't mean Logistic Regression, as I don't assume that the $y$'s are coming from a Bernoulli…
Maverick Meerkat
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Comparison of logit and probit estimations

There are a lot of questions concerning logit and probit relations (led by 20523), but I'm still confused with a seemingly simple issue. On the one hand, often we see that for 'rule-of-thumb' correction of $\beta$ in logit and probit people use…
garej
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Is there a connection between the normal and the logistic distribution?

Regarding Bayesian statistics I found in a script that there is such link, and the logistic arises in context of a normal distribution and a "binary state". However, I have no idea what is the meaning behind this. And I found no further hints. The…
user32038
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Obtaining the Log-logistic distribution from a truncated logistic distribution

Let $$f(x) = \frac{e^x}{(1+e^x)^2}~,~ -\infty \lt x \lt \infty~~~~~(1)$$ be the standard logistic pdf of a random variable $X$. Then one can obtain the pdf of the log-logistic distribution via the transformation $$ \log T = Y = a+bX ~,~b\gt 0~,~…
Gorg
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How to compute for Bivariate Logistic Distribution

This is the logistic distribution of single random variable (taken from Wikipedia). $x$ = random variable $\mu$ = mean of all random variables $s$ = variance. Now, I want to do a Bivariate logistic distribution (having two random variables $x_1$…
iamlol
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What is this distribution? Inverted S / cursive N

I have come across a graph pattern in two basically unrelated experiments, and I want to understand where it is coming from, or at least how to handle it statistically. I work in computational linguistics; I have picked up some statistics along the…
tripleee
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Inverse Mills Ratio for Logit?

For $X\sim N(\mu,\sigma^2)$ , $$E[X|X>\alpha] = \mu +\sigma \frac{\phi\left(\frac{\alpha-\mu}{\sigma}\right)}{1-\Phi\left(\frac{\alpha-\mu}{\sigma}\right)} $$ Is there an analogous expression for when $X$ is distributed logistically?
Michael Gmeiner
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