# Questions tagged [logistic-distribution]

A symmetric distribution which CDF is the logistic function.

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### Logistic regression - Confidence interval for x axis

My question is very similar to the post Confidence interval for x-values given a probability in a logistic regression where ultimately no answer was given. I have also posted a similar version on the ...
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### Where does the Logistic Distribution get its name?

Having read around on the topic I understand its application as a close approximation of the normal distribution with a nicer mathematical form, but where does its name come from? Is it associated ...
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### Logistic Regression vs Random Forest

I have a dataset with a binary dependent variable and 6 dependent variables. I performed logistic regression and random forest and the AUC is higher for Logistic Regression. I would like though to ...
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### Multinomial Logistic Regression as a latent variable model

I was reading the wiki entry for multinomial logistic regression https://en.wikipedia.org/wiki/Multinomial_logistic_regression#As_a_latent-variable_model and it states that we can view the multinomial ...
143 views

### Logistic distribution's minimal sufficient statistics

Distribution function(pdf) is If x is sample from population, f(x|θ) is I calculated f(x|theta)/f(y|theta), but I don't know how can I find minimal sufficient statistics.
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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 ...
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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 ...
1 vote
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### Is the Hodges-Lehmann estimator 'optimal' for estimating the location parameter of Logistic distribution?

Is the Hodges-Lehmann estimator $\hat\theta_{HL}=\operatorname{median}\limits_{1\le i\le j\le n}\left\{\frac{X_i+X_j}{2}\right\}$ in some sense 'optimal' for estimating the location parameter $\theta$ ...
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### Are their feature selection always go by linear model?

A generalized linear model maps a linear transformation of features to some response through monotonic function, does GLM feature selection always go by analyzing the coefs of this linear ...
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### Trade-off between omitting variables or dropping observations in multivariate logistic regression

Say you are selecting $n$ observations from a complex survey of $N$ individuals to create an analytical sample of relevant observations; and that you intend to fit a binomial multivariate logistic ...
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### What are the preliminary analysis before running a logistic regression?

I have a dichotomous variable which represents if a student is accepted or not in a University. In order to do this I have about 60 variables (information of the students: gender, age, etc; their ...
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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 ...
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### Method of moments and MLE

Suppose a random variable follows the logistic distribution, $X ∼ Logistic (\mu, \sigma)$ and we restrict our attention to random samples drawn from this random variable $X$. What would be the MoM and ...
264 views

### When should you not use logistic regression GLM with a binary response variable?

I came across a set of data that does not seem to "flip" from 0 to 1 (binary response variable) when the predictor variable increase. Thus, this is the plot I got after plotting the ...
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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' ...
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1 vote
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### How to invert a mixture of log-logistic distributions? [duplicate]

Say I have a CDF of the form $$F(x) = \sum_{i=1}^n \frac{ k_i }{ 1 + (x/\alpha_i)^{ - \beta_i } }$$ $$\sum_{i=1}^n k_i = 1$$ How do I find the quantile function, i.e. how do I invert F for n>1? I ...
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### How to specify a risk model?

I'm reading this article. The authors indicated that for a random sample of 12 characteristics and 3600 patients affected in two arms (control and treatment arm), they fitted a risk model consisting ...
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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 ...
1 vote
94 views

### Independent variables should have exponential distribution in logistic regression

As per my understanding of logistic regression, a log of odds of the desired value of “y” should be in linear relation with the log (x). Does that mean that independent variables should have ...
198 views

### Location and scale estimation for log-logistic in scipy

I have to estimate the location and scale parameters for a log-logistic or fisk distribution using scipy. The shape parameter is already defined and I would like to estimate loc and scale parameter ...
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### How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ for the logistic distribution?

Take the cumulative distribution function (cdf) $\Phi(z) = \frac{1}{1+\exp(-z)}$ and probability density function (pdf) $\phi(z)=\Phi(z)(1-\Phi(z))$ of the logistic distribution. How can one calculate ...
1 vote
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### Logistic Regression For Classification [duplicate]

The origin of logistic regression is actually logistic curve which varies from the value 0 to the value 1. It looks like the letter S, and it specifies the growth of species. If our data distribution ...
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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 ...
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### Infinite continuous response variable for logistic distribution? GLMM

When I would like to use the generalized linear mixed model (GLMM) for my data analysis, I would have to check the distribution of the response variable so as to decide the link-function. The result ...
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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 ...
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### Logistic Regression Models Without Main Effects?

I am building logistic regression models measuring human behaviour, which consist of categorical variables: demographics, conditions, and interactions between the demographics and the condition ...
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### Getting logistic distribution from student's t-distribution

How can I get the probability density function (PDF) of standard logistic distribution from the PDF of symmetric student's t-distribution with location and scale parameters. In the $(\beta_1, \beta_2)$...
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### Use of KS statistics to choose the probability cut-off in logistic regression model [closed]

I was doing some reading on choosing the score cut-off of a logistic regression model using the KS-Stats. Suppose I fitted a logistic regression model on the train data and now want to decide the ...
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291 views

### interpretation of logistic coefficient

I have some toy data for an experiment where subjects are shown pictures A,B and C and then they are given a choice between choice A or choice B. I am interested in determining the effect of the ...
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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 ...
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