Questions tagged [lognormal]

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

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44
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3answers
15k views

Which has the heavier tail, lognormal or gamma?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation with the same person.) Last year I was told that the gamma distribution is ...
53
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3answers
35k views

Linear model with log-transformed response vs. generalized linear model with log link

In this paper titled "CHOOSING AMONG GENERALIZED LINEAR MODELS APPLIED TO MEDICAL DATA" the authors write: In a generalized linear model, the mean is transformed, by the link function, instead of ...
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3answers
5k views

Difference of two i.i.d. lognormal random variables

Let $X_1$ and $X_2$ be 2 i.i.d. r.v.'s where $\log(X_1),\log(X_2) \sim N(\mu,\sigma)$. I'd like to know the distribution for $X_1 - X_2$. The best I can do is to take the Taylor series of both and ...
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1answer
5k views

Whether distributions with the same moments are identical

Following are similar to but different from previous posts here and here Given two distributions which admit moments of all orders, if all the moments of two distributions are the same, then are they ...
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2answers
588 views

How to find normal and lognormal moments, given partial information?

$Y=\ln(X)$. $X$ is lognormal and $Y$ is normal. If all I know is the arithmetic mean of $Y$ and the standard deviation of $X$. What is the formula to calculate the arithmetic mean of $X$ and the ...
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3answers
18k views

How do I calculate a confidence interval for the mean of a log-normal data set?

I've heard/seen in several places that you can transform the data set into something that is normal-distributed by taking the logarithm of each sample, calculate the confidence interval for the ...
20
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1answer
34k views

Expected value and variance of log(a)

I have a random variable $X(a) = \log(a)$ where a is normal distributed $\mathcal N(\mu,\sigma^2)$. What can I say about $E(X)$ and $Var(X)$? An approximation would be helpful too.
16
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1answer
16k views

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
20k views

Gamma vs. lognormal distributions

I have an experimentally observed distribution that looks very similar to a gamma or lognormal distribution. I've read that the lognormal distribution is the maximum entropy probability distribution ...
8
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1answer
2k views

MLE/Likelihood of lognormally distributed interval

I have a variable set of responses that are expressed as an interval such as the sample below. ...
19
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5answers
35k views

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
31k views

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 ...
19
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4answers
3k views

What exactly are moments? How are they derived?

We are typically introduced to method of moments estimators by "equating population moments to their sample counterpart" until we have estimated all of the population's parameters; so that, in the ...
11
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1answer
20k views

How to calculate a mean and standard deviation for a lognormal distribution using 2 percentiles

I am trying to calculate a mean and standard deviation from 2 percentiles for a lognormal distribution. I was successful in performing the calculation for a normal distribution using ...
4
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2answers
262 views

What is the best point forecast for lognormally distributed data?

I believe that the values I am forecasting are lognormally distributed with log-mean $\mu$ and log-variance $\sigma^2$. I need a point forecast (i.e., a one-number summary) that minimizes the expected ...
11
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4answers
20k views

The sum of independent lognormal random variables appears lognormal?

I'm trying to understand why the sum of two (or more) lognormal random variables approaches a lognormal distribution as you increase the number of observations. I've looked online and not found any ...
11
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1answer
9k views

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 $\...
10
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3answers
7k views

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 ...
8
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1answer
4k views

Can I get the parameters of a lognormal distribution from the sample mean & median?

I have the mean and median values for a sample drawn from a lognormal distribution. Note that this is not the mean and median of the logs of the variable, though I can of course calculate the logs of ...
6
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1answer
752 views

Covariance between a normally distributed variable and its exponent

Given $X \sim \mathcal{N}(\mu,\,\sigma^{2})$, what is the covariance between $X$ and $e^X$?
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1answer
2k views

Is the product of multivariate lognormal distributions is multivariate lognormal distribution

A. Mulitivariate normal distribution case with latent variable $X$ Mapping from the low-dimensional space $X$ in Q-dimensional space (Q=2) to the high-dimensional space of $Y$ in D-dimensional space (...
5
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1answer
2k views

How to transform one PDF into another graphically?

To understand what I mean, let's use two well-known distributions: the normal and lognormal ones. From the dataset point of view, if you take normally-distributed data and take their exponential, you ...
7
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1answer
9k views

Expectation, Variance and Correlation of a bivariate Lognormal distribution

If $Y \sim N(\mu,\sigma^2)$ is normally distributed, then $X=\mathrm{e}^Y$ is lognormally distributed. To get the log-$\mu$ and log-$\sigma$ of this lognormal distribution you calculate $$\sigma^2 = \...
5
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2answers
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How to calculate Estimated Arithmetic Mean for a lognormal distribution

I have been tasked to program functions from some Excel sheet into a asp.net app so it can be shared to my colleagues via a web interface. However, I am stuck on one thing. I have a set of variables $...
4
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1answer
2k views

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 ...
3
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3answers
921 views

Quantify Difference/Distance between Lognormal distributions

I am trying to determine a metric that quantifies the distance between two continuous lognormal distributions. The data is actually a mixture of two lognormal distributions (I am not sure if this can ...
25
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2answers
2k views

Bias of moment estimator of lognormal distribution

I am doing some numerical experiment that consists in sampling a lognormal distribution $X\sim\mathcal{LN}(\mu, \sigma)$, and trying to estimate the moments $\mathbb{E}[X^n]$ by two methods: Looking ...
5
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2answers
9k views

Interpreting test results on log-transformed data

I have data that is not normally distributed. I can log-transform it to be normally distributed, and then perform, for example, a t-test. But how do I interpret the results of the t-test? Do I have ...
6
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2answers
44k views

Plot log-normal distribution in R [closed]

I need to plot lognormal distribution with mean 1 and variance 0.6 in R. I tried to do this using rlnorm function in ...
4
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1answer
7k views

Multivariate log-normal probabiltiy density function (PDF)

The Multivariate Gaussian pdf is given by $$(2\pi)^{-\frac{K}{2}} \det(\Sigma)^{-\frac{1}{2}} \exp({-\frac{1}{2}}(X-\mu)' \Sigma^{-1} (X-\mu)) $$ The wikipedia for multivariate Gaussians is here ...
7
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1answer
2k views

Finding the distribution of sum of Lognormal Random Variables

I am trying to find the distribution of sum of 2 lognormal random variables. I referred the literature available on Cross validated, Stack overflow and few papers before posting this. I used ...
6
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2answers
8k views

Lognormal Regression?

I'm trying to model a lognormal response variable. I want to take the log of the response variable and do a least-squares regression line over my predictive variable. However, I'm worried about this....
5
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2answers
2k views

Lower and Upper confidence limit on estimated arithmetic mean using Land's exact procedure

I have to compute the LCL95% and UCL95% using Land's "exact" method. I computed the LCL and UCL for this lognormal distribution using another technique and I can't find anything for Land's exact ...
6
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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 ...
5
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2answers
1k views

Common name for distributions that are bounded on one side

Is there a common name to refer to distributions that are bounded on one side, and unbounded on the other side? For example, log-normal distribution, where the minimum value is zero, the maximum is +...
2
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1answer
1k views

KL divergence of multivariate lognormal distributions

I've been trying to get the KL divergence for two lognormal distributions. I know what it is for the univariate case, $$ D(f_i\|f_j)= \frac1{2\sigma_j^2}\left[(\mu_i-\mu_j)^2+\sigma_i^2-\sigma_j^2\...
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1answer
2k views

Multiplicative error and additive error for generalized linear model

If the following generalized linear model was used, how should I interpret the error term? link function: natural log distribution: Gamma distribution i.e., $\ln E(Y)=X\beta$ and $E(Y)=\exp(X\beta)$ ...
5
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2answers
13k views

How can I convert a lognormal distribution into a normal distribution?

I have a sample of data that follows a lognormal distribution. I would like to represent the distribution as a "Gaussian" histogram and overlayed fit (along a logarithmic x-axis) instead of a ...
4
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2answers
3k views

Moment Generating Function for Lognormal Random Variable

I'm working through the proof of a lognormal random variable and am having some difficulty in moving through it. I understand the following: Our CDF is $\Phi(\frac{logx - \mu}{\sigma})$, and thus our ...
3
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1answer
22k views

Calculate variance and standard deviation for Log Normal Distribution

I am trying to calculate the variance and standard deviation for a log normal distribution. I was able to calculate the mean after reading this stack exchange article How to calculate a mean and ...
2
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1answer
1k views

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 ...
24
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1answer
30k views

Why stock prices are lognormal but stock returns are normal

Except for the fact that returns can be negative while prices must be positive, is there any other reason behind modelling stock prices as a log normal distribution but modelling stock returns as a ...
11
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3answers
30k views

How to check if my data fits log normal distribution?

I'd like to check in R if my data fits log-normal or Pareto distributions. How could I do that? Perhaps ks.test could help me do ...
9
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1answer
11k views

When is it OK to write “we assumed a normal distribution” of an empirical measurement?

It is ingrained in the teaching of applied disciplines, such as medicine, that measurements of bio-medical quantities in the population follow a normal "bell curve." A Google search of the the string "...
13
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1answer
5k views

Why is ln[E(x)] > E[ln(x)]?

We're dealing with the lognormal distribution in a finance course and my textbook just states that this is true, which I find sort of frustrating as my maths background isn't very strong but I want ...
8
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1answer
2k views

When to use sample median as an estimator for the median of a lognormal distribution?

I myself would always use geometric mean to estimate a lognormal median. However, in the industry world, sometimes using the sample median gives better results. The question thus is, is there a cutoff ...
7
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1answer
9k views

The product of two lognormal random variables

Let $X_1$ and $X_2$ be two normal random variables. Write $X_1\sim N(\mu_1, \sigma^2_1)$ and $X_2\sim N(\mu_2, \sigma^2_2)$, to fix ideas. Consider the corresponding log-normal random variables: $...
7
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3answers
8k views

Can quantiles be calculated for lognormal distributions?

I just talked to someone who stated that quantiles cannot be computed for lognormal distributions. or it does not make sense. Is this true?
6
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1answer
2k views

Robust parameter estimation for shifted log normal distribution

I have a data set which fits a logNormal distribution quite well. (From a theoretical point of view, it is some hard-to-tackle quotient distribution). However, the data is quite dirty, so parameter ...
5
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1answer
1k views

Goodness of fitting: power-law or discrete log-normal?

I have a dataset of users' check-ins of a social network. I'm verifying if these data are distributed according to a power-law distribution. To check this I used the function ...