Questions tagged [lognormal]

A lognormal distribution is the distribution of a random variable whose logarithm has a normal distribution.

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If $X$ has a log-normal distribution, does $X-c$ also have a log-normal distribution?

Let's say $X$ has a log-normal distribution and there is one real positive number $c$. then is it right to say that $(X -c)$ also has some log-normal distribution? My feeling is that, it can't be, ...
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Parameters’ uncertainty for small sample size

Suppose we have a small set of numbers (5 to 10 observations), and we’re trying to fit a distribution to this set. Also, we know that all numbers are positive. I tried to fit lognormal, but I’m not ...
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3answers
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Priors for log-normal models

I am trying to determine what the most appropriate non-informative priors are for the two parameters of a log-normal distribution (for an accelerated failure time model). I had been working with a ...
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1answer
3k views

How to fit a multivariate lognormal distribution to a given dataset

Given a dataset X with N observations in 11 dimensions, where each variable is restricted to be >= 0, how is it possible to fit an 11-dimensional log-normal distribution to this dataset? I only found ...
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2answers
750 views

Arbitrariness of Euler's number in exponential of log-normal distribution

The Wikipedia article of the log-normal distribution says If $X$ is a random variable with a normal distribution, then $Y = \exp(X)$ has a log-normal distribution; likewise, if $Y$ is log-...
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1answer
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How do I make power computation for testing differnce between two log normal means with R? [closed]

I want to do power computation for testing differnce between two log normal means with R. Can you write using R code? best wishes...
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5answers
13k views

Interpreting the difference between lognormal and power law distribution (network degree distribution)

First off, I'm not a statistician. However, I have been doing statistical network analysis for my PhD. As part of the network analysis, I plotted a Complementary Cumulative Distribution Function (...
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2answers
10k views

How do I estimate the parameters of a log-normal distribution from the sample mean and sample variance

Given the sample mean $\bar{x}$ and the sample variance $s^2$ of a random variable $X$, is it possible to estimate the shape $\sigma^2$ and log-scale $\mu$ of the log-normal distribution, with ...
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Mean and variance of log-binomial distribution

If X is a random variable with a normal distribution, then Y = exp(X) has a log-normal distribution. Likewise if X is a random variable with a binomial distribution, then Y = exp(X) has a log-...
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1answer
595 views

Sum of lognormal distributed insurance claims

For a method calculating expected claims in insurance I have to assume lognormal distribution. For testing I would use annual cumulated data. With a small sample capped at 20 years, my idea is to use ...
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Is a log transformation a valid technique for t-testing non-normal data?

In reviewing a paper, the authors state, "Continuous outcome variables exhibiting a skewed distribution were transformed, using the natural logarithms, before t tests were conducted to satisfy the ...
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1answer
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Base-10 lognormal PDF integrated over log10(x)

From what I understand, the lognormal probability density function in base-10 is mathematically defined thus: $$ p(x; \mu, \sigma) = \frac{log_{10}(e)}{x \sigma \sqrt{2 \pi}} e^{-\frac{(log_{10}(x) -...
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Can lognormal + constant be still considered lognormal?

In one of my computations (result of GLM with some model values replaced with observations) I resulted with a distribution that is a lognormal distribution plus some constant. Can I still speak of ...
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5answers
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How to specify a lognormal distribution in the glm family argument in R? [closed]

Simple question: How to specify a lognormal distribution in the GLM family argument in R? I could not find how this can be achieved. Why is lognormal (or exponential) not an option in the family ...
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2answers
863 views

For lognormal data, what are necessary sample sizes for a difference in means between treatment / control

Given a population to be divided between treatment / control, if I believe a variable is distributed lognormal in the population, how do I know what the necessary control size is in order to guarantee ...
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1answer
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Lognormal distribution using binned or grouped data

I understand the Max likelihood estimators for mu and sigma for the lognormal distribution when data are actual values. However I need to understand how these formulas are modified when data are ...
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1answer
925 views

Approximating lognormal sum pdf (in R)

I have an application for which I need an approximation to the lognormal sum pdf for use as part of a likelihood function. The lognormal sum distribution has no closed form, and there are a bunch of ...
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1answer
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Upper/lower bound and initial domain for lognormal distribution

I'm trying to implement logNormal distribution into my java program because lognormal dist doesn't exist into apache commons math library. I have no problem to re-write density and cumulative ...
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1answer
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Is it possible to analytically integrate $x$ multiplied by the lognormal probability density function?

Firstly, by analytically integrate, I mean, is there an integration rule to solve this as opposed to numerical analyses (such as trapezoidal, Gauss-Legendre or Simpson's rules)? I have a function $\...
4
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1answer
447 views

Means and imputation of log-normal variables

The geometric mean is the appropriate measure of central tendency for log-normally distributed variables. However, the arithmetic mean still has some use in relation to log-normal variables - in ...
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2answers
571 views

Logarithmic regression with individual errors

If I have a dataset of $N$ pairs ($x_i$,$y_i$) where each $y_i$ has an individual error $\sigma_{y_i}$, I can incorporate this into regression by using the inverse of this as weights. If I now do ...
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1answer
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Correlation of log-normal random variables

Given $X_1$ and $X_2$ normal random variables with correlation coefficient $\rho$, how do I find the correlation between following lognormal random variables $Y_1$ and $Y_2$? $Y_1 = a_1 \exp(\mu_1 T +...
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2answers
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Log normal distributions - particle sizes in an aerosol

Statistics were never my strong point and it's my first question, so please be gentle :) I'm doing some research using Computational Fluid Dynamics, CFD, to model the flow of an oil aerosol through a ...

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