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

learn more… | top users | synonyms

0
votes
0answers
11 views

The distribution of a product between a Lognormal and a Beta is …?

I have to random variables expressed as $1 \times 1000$ vectors. One of the vectors $B$ is Beta distributed while the other $L$ is lognormal distributed. Upon element-wise multiplication, I get vector ...
0
votes
0answers
22 views

Estimating the variance of a sum of predictions

I have $N$ plots that were used to estimate a relationship between three predictor variables, $X_1$, $X_2$, $X_3$, and an outcome, $Y$, using a generalized linear (lognormal) model. The resulting ...
0
votes
0answers
14 views

Find the mean of lognormal rv's with available variance and the sum of rv's

I have the sum of a bunch of random variables $S$, v = [1 1 2 2 3 3 4 ...]; S = sum(v); I know that vector $v$ is lognormally distributed, BUT I DON'T KNOW IT. ...
1
vote
1answer
65 views

How to describe a function of two normal distributed random variables

I consider the generic problem $W(X,Y)=-2\ln(\frac{(X-Y)^2}{2(X^2+Y^2)})$ where $X$ and $Y$ are normally distributed random variables Can I make any statements about the distribution of $W$?
1
vote
1answer
37 views

Regression against polynomials and log-linear predictors

I have a regression problem where one of the predictors has a very good fit as $Y \sim poly(X_1, 2)$. However, $Y$ is clearly log-linear against my second predictor $X_2$, so $ln(Y) \sim ln(X_2)$. ...
0
votes
1answer
58 views

How to estimate parameters of a log-normal distribution?

I am using income data from the Current Population Survey for a small undergrad economics paper. In economics, there is evidence that the income of 97%–99% of the population is distributed ...
1
vote
1answer
15 views

Gamma Distribution with Percentages

I am dealing with a set of data that appears to follow a gamma distribution or a lognormal distribution but the only issue is that the data set is in percentages and both of these distributions don't ...
0
votes
0answers
62 views

Percent change interpretation in log-transformed regression: Percent change from what?

I am dealing with a regression model where both the DV and IV are log-transformed. I have found this explanation of how to interpret the effects (both in the Cross-Validated hyperlink and in ...
0
votes
0answers
9 views

Continuous distribution for discrete population: Assessment?

We model Inflow and Outflow [people per day] by means of stochastic processes. We would like to assess to what extent the resulting continuous distributions acceptably model the discrete variables. ...
3
votes
1answer
33 views

Forming Location-Scale Family for Log-Normal

For the random variable X with a log-normal pdf $f(x)=\frac{1}{\sqrt{2*\pi}}x^{-1}e^{-.5*log(x)^2}$ I am trying to find a location-scale family $h(x)$ such that $h(x)$ has mean 0 and variance 1 Now ...
2
votes
2answers
36 views

Distribution of proportions relative to sum of random variables

Let $X_1,...,X_n$ be iid lognormally distributed variables and $X_{sum} = X_1+...+X_n$. What is the distribution of $\frac{X_k}{X_{sum}}$ for each $k$ in $1..n$? What are their density functions? ...
2
votes
1answer
88 views

Mixture of Gaussians on Log of Data

I am practicing Mixture of Gaussians and found the below dataset snoq, which is the precipitation amounts recorded at a US region, with ...
0
votes
0answers
22 views

Combining two data sets with different weightings, possibly Bayesian Updating?

I am a PhD student and I am currently looking at railway track degradation. As part of this I am finding linear fits of the track geometry recordings against time to give a degradation rate. The ...
0
votes
0answers
8 views

Finding significant values in my tree-like distributed data

i have a question about my data. Let me first describe what i know about it. I know that the number of data points I have is large (200-1000) I know each data point value is greater or equal to 0 I ...
1
vote
1answer
49 views

Tests for lognormal distribution

I have some data in the following manner. 10 3 4 5 6 9 ... I have to check that the difference between returns is log normal by doing ln(return/previous return). I know some tests for normality if i ...
1
vote
1answer
29 views

Error propagation - nonnormal (again)

I have a dataset of ~2000 points. Each of those points has a standard error value associated with it, and it is assumed that the data points and errors are uncorrelated. Both the dataset and the ...
4
votes
1answer
71 views

KL divergence between a gamma distribution and a lognormal distribution?

Is there a closed-form formula for the following KL divergence? $D_{KL}(X,Y)$ where $X \sim \mathrm{Gamma}(k,\theta)$ and $Y \sim \mathrm{LogNormal}(\mu,\sigma^2)$
2
votes
1answer
26 views

Finding a distribution for data in $\mathbb{N}_0$

Suppose, we have a set of 10,000 individuals. Each individual falls into exactly one of 200 categories. [Edit: The categories are phenotypes (different potential outcomes) of the one property that is ...
2
votes
1answer
116 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 = ...
4
votes
1answer
29 views

Constant default probability in Merton Model

The Merton model says we have a geometric brownian motion $V(t)$ with drift $\mu$ and volatility $\sigma$. Thus $$V(t)=V(0) \exp\left(\sigma W(t)+(\mu-\frac{1}{2}\sigma^2)t\right)$$ where $W(t)$ is a ...
2
votes
3answers
73 views

Mean test of log-normal distibutions

I have two data sets, which are assumed to be log-normally distributed. How can I test whether their means are statistically different from each other? I guess I cannot use the 2-sample t-test, ...
1
vote
3answers
55 views

Remapping the Sum of two Normal Random variables?

I have a problem where I have sum of two random variables 1). Each distributed independently normally with different means ($\mu_1$, $\mu_2$) and sds ($\sigma_1$, $\sigma_2$). $Z=R_1+R_2$ 2). Each ...
0
votes
1answer
155 views

Interpreting negative binomial regression with log transformed independent variables

My independent variables were highly skewed, so to normalise the distribution they were log transformed. Also since there were zeros in the data, I've added + 1 to transform the variables. This is ...
1
vote
1answer
18 views

Picking a probability distribution for observed intensities

I have an experiment that measures "intensity" (in this case, electron density of a molecule) on a grid. The values it gives are non-negative,. I'd like to write a likelihood for this observation ...
1
vote
0answers
36 views

Problem with multivariate lognormal distribution in R

I'm using the R package compositions for the multivariate lognormal distribution. this is the only package I found that supports it. However I'm not sure how this ...
1
vote
1answer
38 views

simulating two correlated lognormal AR(1) time series

I'd like to simulate 2 correlated lognormal AR1 time series. I have already found this post which is the answer for 2 Normal AR1 time series How to simulate two correlated AR(1) time series? I've ...
5
votes
1answer
330 views

Why stock prices are lognormal but stock returns are normal

Except for the fact that returns can be -ve while prices must be +ve, is there any other reason behind modelling stock prices as a log normal distribution but modelling stock returns as a normal ...
1
vote
0answers
86 views

Use of normality test to distinguish gamma from log-normal distribution

I have random population sample data that I would like to describe using a distribution. If I plot the estimated kernel density, the data appear positively skewed and using functions in R such as ...
0
votes
0answers
181 views

Sample size calculation for non-normal data (possibly lognormal)

I am currently trying to rack my brains to find a solution but I seem to be coming up with nothing. I have water quality data with which I want to get a sample size calculation from for a future ...
0
votes
0answers
29 views

Fundamental Issues with Influence weighted resampling for bootstrapped predictions

I have a large database 1mill+ from which it is known that there are many influential points and outliers. I am interested in generating a series of predictions from subsets (1,000+) of the data and ...
1
vote
0answers
289 views

A log-normal distribution in Python

I have seen several questions in stackoverflow regarding how to fit a log-normal distribution. Still there are two clarifications that I need known. I have a ...
2
votes
0answers
63 views

Fitting two different mixture distributions

is there a package in R to fit two different mixture distributions in R ? Let's say I want to fit a mixture of power law distribution and lognormal distribution. Is this possible ? I know you can fit ...
0
votes
1answer
42 views

Help interpret Distribution of Wlan Signal Strength Measurements

For my project I need to evaluate large amounts of wlan signal strength measurements. Measurement is in dBm which is a logarithmic scale for milli watt (so every 3dBm the milliwatts double) where ...
0
votes
1answer
76 views

Log-normal random variables and the distribution of shocks in AR(1) model

Assume, X and Y are jointly lognormally distributied and let X follow AR(1) process: $$X_{t+1} = \mu_t + \alpha X_t+ u_{t+1},$$ $\alpha < 1$. Thereafter, I can't come up with an answer to the two ...
2
votes
1answer
98 views

Sampling under assumption of log normal distributed data with sample mean and standard deviation

I have the sample mean and the sample standard deviation of income calculated from individual tax data of all citizens in country (let's call this data X). I do not have access to this tax income ...
3
votes
2answers
103 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 ...
3
votes
0answers
78 views

Interpretation of log transformed predictor in negative binomial regression

I mainly want to make sure that I'm making the correct interpretation here. I built a negative binomial regression model predicting a count variable. There was evidence of overdispersion or I would ...
1
vote
0answers
50 views

Plotting raw data, but running statistics on log-transformed data

My data is non-normal, I want to show my raw data, in a scientific journal, by median +/- mad, to show the true nature of the data. However, if log-transformed, the data is normal. Can I then ...
1
vote
0answers
77 views

On log-normal distributions

Since my research data seems to follow log-normal distribution, I was curious to learn more about the topic. In addition to very nice answers here on Cross Validated (In linear regression, when is it ...
1
vote
1answer
243 views

convert lognormal Cumulative Density Function P90 and P10 values to mean and sigma [duplicate]

Practioners are used to defining lognormal distributions in terms of P90 and P10 cumulative density function values. To utilize these esperts' input I need to be able to convert these P90/P10 values ...
1
vote
1answer
555 views

R: random sampling for multivariate normal and log-normal distributions

I want to generate random monthly (m) temperature (T) and Precipitation (P) data considering that both variables are intercorrelated (rTP[m]) The tricky thing is that my random variables that have ...
0
votes
0answers
28 views

Terminology and handling of log-normal mixture distributions

The definition of a log-normal distribution of a random variable is based on normality of its logarithm. I'm curious whether there exist a specific term for cases, where log-transformed data does not ...
0
votes
1answer
411 views

Summarizing a lognormal distribution with geometric mean and standard deviation

I have some data that I strongly suspect are lognormally distributed, and I'd like to summarize the distribution using the mean and standard deviation. I've read that with lognormal distributions the ...
1
vote
1answer
355 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 $E(Y)=\exp(X\beta)$ ...
4
votes
2answers
309 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 ...
3
votes
0answers
117 views

Boxplots with lognormally distributed data

Context Environmental data (e.g., pollutant concentrations in water, soil, air) are often lognormally distributed. Even when they are not, we tend to assume that they are (for better or worse). ...
1
vote
0answers
29 views

Proper back-transformation of lognormal standard deviation to find confidence intervals around a mean [duplicate]

I want to determine the 95% confidence interval of a mean. I logged-transformed my data in order to achieve a normal distribution. Several observations contained 0, so I changed these to 1 so that ...
4
votes
3answers
171 views

Estimating the ratio of cell means in ANOVA under lognormal assumption

I am conducting a two-sample test (1-way ANOVA with 2 treatments), and the goal is to estimate the ratio of cell means assuming that the data are lognormal. A simple approach is to log the response ...
1
vote
1answer
263 views

Sampling from a lognormal distribution

Suppose we are given $\mu$ and $\sigma$ for a lognormal distribution with random variable $X$. $\mu$ is the mean of the variable's logarithm and $\sigma$ is the standard deviation of the variable's ...
1
vote
0answers
28 views

How to get the values for the graph of confidence limit for the exceedance fraction vs z-value?

I am working on an application for a team of industrial hygienists and I need to create a lookup function for the confidence limit for the exceedance fraction. I found what I need from this book: ...