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

learn more… | top users | synonyms

1
vote
0answers
27 views

Expected value log-normal variable

Suppose $X_t$ and $Y_t$ are bivariance have standard normal distributions with mean zero and variance 1. The covariance of $X_t$ and $Y_t$ is $Cov_t(X_t, Y_t) = c$, where $c$ is a constant. What is ...
1
vote
0answers
16 views

How should I transform a featureset (15000 variables) that is mostly presence/absence, but present values are lognormal distributed?

I am trying to learn machine learning and have a nice featureset with a binary classification. The dataset is 15000 variables and 2500 data rows. For every data row, almost all variables are 0, and ...
1
vote
2answers
170 views

What is the distribution of $e=Y-\mathbb{E}(Y)$ where $Y=\exp(u), \ \ \ u\sim\mathbb{N}\left(\mu,\sigma^2\right)$

As $Y$ is log-normal we've $Y\sim \mathbb{LN}\big(\exp(\mu+\sigma^2/2),\exp(2\mu+\sigma)(\exp(\mu^2)-1)\big)$. Now I define $e = Y - \mathbb{E}(Y) = Y - \exp(\mu+\sigma^2/2)$. As $e$ is the ...
0
votes
1answer
83 views

Negative variance in a log normal distribution

I'm currently trying to solve a maximum likelihood estimation of a random variable which is assumed to be log normal distributed. For this I compute the log of all sample values I have in order to ...
0
votes
1answer
46 views

log hazard function in R

I'm trying to write out the log hazard function of the lognormal distribution and use this in R. Using the survival function: and the hazard function: I have the following for the log(hazard): ...
-1
votes
1answer
51 views

How do I determine parameters of normal & lognormal distribution given two points?

Assume I have two values which represent two quantiles for the same lognormal and/or normal distribution. How can I determine the parameters of the distribution? ...
2
votes
1answer
36 views

Calculating actual quantile from poorly defined lognormal distributions

I have a dataset in which the uncertainties in various parameters are modelled with a lognormal distribution. After the experiment I get a single number result. As part of a lookback to understand how ...
0
votes
1answer
34 views

How to interpret confidence intervals from R t.test when log transforming the data

I have a quite large dataset that contains the time it took to make two different types of requests over a network. I would like to calculate how big the difference between the two types are. I was ...
4
votes
1answer
99 views

lognormal with very large mean, but small sample value

Let $X \sim N(\mu, \sigma^2)$, where $\mu = -800$ and $\sigma = 76$ Let $Y = \exp(X)$, so Y has a lognormal distribution, $E(Y) = \exp(\mu + \sigma^2/2) = \exp(2088)$, which is a very large number. ...
2
votes
1answer
52 views

Name for exp(log normal) distribution

If the log of a dataset fits a normal distribution, then the data is said to be log normal. If the log of a dataset fits a log normal distribution, is the data said to be log log normal? Is there a ...
-1
votes
1answer
70 views

Transformation from Normal to LogNormal in R

I need to generate random numbers from LogNormal distribution by using transformation with Normal. Although I tried some way, it didn't work. How can I make it ?
1
vote
0answers
50 views

Taylor Expansion of Power of Cumulative Log Normal Distribution Function - Show Lagrange Remainder tends to Zero

QUESTION I am looking to find a simplification of the expression below. I have attempted this using the Taylor series. The question then remains if we can show the Lagrange remainder goes to zero. I ...
0
votes
0answers
17 views

Is there any paper about the distribution of difference of log-normal variable?

I am working on the problem relating to the difference of log-normal distribution. I have found several papers about this topic, however, none of them gives me the answer I want. More specifically, ...
0
votes
0answers
22 views

Log Transformations and Z-Scores

I have some skewed variables in my dataset, I did log-transformations to make them more normal. Do I now turn them into z-scores if I am running analysis with other standardized variables in my ...
11
votes
1answer
150 views

Approximating $\log( E(X))$

I was casually reading an article (in economics) which had the following approximation for $\log(E(X))$: $\log(E(X)) \approx E(\log(X))+0.5 \mathrm{var}(\log(X))$, which the author says is exact if ...
1
vote
0answers
41 views

How to pre-process data for partial least square PLS regression in R?

I have a data frame that is consisted of 20 observations and 35 variables. I want to prepare the data for partial least square regression PLS in R. Many authors suggest: 1)Check whether the ...
1
vote
1answer
54 views

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

I'm not a statistician, so I would be grateful if someone can help me with my questions. I have a dataset of users' check-ins of a social network. I'm verifying if these data are distributed ...
2
votes
1answer
58 views

Variance for arbitrary power of log normal variate

Say we have a R.V. called $X$ and let $\ln{X} \sim N(\mu, \sigma^2)$, therefore $X$ follows a Log Normal distribution. Then let another R.V. $Y = X^{\gamma}$, where $\gamma$ is just a constant. Does ...
5
votes
1answer
151 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 ...
0
votes
0answers
20 views

Conditional expected value for dependent Log-normal Distribution

I'm trying to find the expected value of a FX derivative which is log normally distributed, dependent on another derivative, but do not have the direct co relation between them. Instead I'm given the ...
1
vote
1answer
415 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
votes
1answer
55 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 ...
3
votes
1answer
69 views

How to find expected value for this financial expression

I am reading a research paper, and there is such condition: $$ E_t\Big[\frac{(F_t - S_{t+1})P_t}{S_tP_{t+1}}X\Big]=0 $$ where $E_t$ is expected value. I suspect that $E_t[F_t] = F_t$ because this ...
3
votes
0answers
45 views

Fitting datas, lognormal and beta distribution, interpretations

I've been given some data that should come from a lognormal distribution. I've got some issues concerning the fitting, here's what I did. ...
1
vote
1answer
94 views

Three parameter lognormal distribution

I'd like to know what results there are for (1-X)(1-Y) where X and Y are independent and both have a lognormal distribution. I'd like to find an analytic solution or closed form approximation, since ...
0
votes
0answers
29 views

Distribution of the ratio of unidimensional samples

I am trying to assess the ability of a transport model to predict the trip times on a network. I have data for a series of trips (each one of a different trip class, e.g. shopping trip, commuting trip ...
0
votes
0answers
34 views

Under what circumstances will the log of a variable be normal, given that the variable is not normal

Let us say there is a variable that is not normally distributed. Under what circumstances will the natural logarithm of the variable be normally distributed? I have seen many articles and papers ...
1
vote
1answer
72 views

R - Same Density but different QQ-Plot?

I have data variable corresponding to quotation amount and I want to find which statistic law this variable follow if there is one. It seems that the ...
1
vote
0answers
35 views

Loss Size Index Function of A Lognormal Random Variable

I have this tutorial question and I've gone through the solutions, getting all but one line of working. I broke down the question to this point but I can't seem to get out the following. So Loss Size ...
0
votes
1answer
41 views

Numerically Solve for Parameters Characterizing Lognormal RV that's Truncated from Above

I am trying to numerically solve for parameters characterizing a lognormal distribution truncated from above with first moment = mean, second moment = ...
0
votes
0answers
70 views

How do I check whether my data fits exponential or lognormal or weibull using chi square and ks tests in R?

I'm a newbie to R language and I need to quickly find whether a set of data I have in a CSV file fits the three distributions Generalized exponential, log normal and Weibull. I need to test it using ...
3
votes
1answer
85 views

kernel density estimation of the log-normal distribution

I stumbled upon the following issue I cannot make sense of: When using default choices, the KDE for a log-normal sample (green) does not look like a density that integrates to 1, compare the true ...
1
vote
0answers
86 views

Distribution of geometric mean of normally distributed independent random variables [closed]

Suppose we have $X(i)$ for $i=1,...,n$ normally distributed independent random variables with the same known $\mu$ and $\sigma$ for all: $$X(i) \tilde{} N(\mu,\sigma)$$ Suppose that we take the ...
0
votes
0answers
49 views

Adding two distributions with proportional means and standard deviations

I need to know the mean $\mu_z$ and standard deviation $\sigma_z$ of a log normal distribution $Z(\mu_z,\sigma_z)$ which is the sum of two other log normal distributions--$X(\mu_x,\sigma_x)$ and ...
0
votes
0answers
42 views

log normal distributions

Here is my questions: X and Y are random variables that are lognormally distributed. G(Y) is some function of Y. What is the expectation value: < X * G(Y) > This is the expectation value of the ...
0
votes
0answers
93 views

ANOVA on a normally and a log-normally distributed variable: what to transform?

For an analysis of variance the residuals (but not the data?) have to be normally distributed. So, I have two variables, one is normally distributed, one is log-normally distributed, and their ...
1
vote
0answers
34 views

Composing a likelihood function for a convolved normal- and lognormal- dataset

I am trying to use some implementation of MLE to solve for the parameters of a mixed normal and lognormal population, and have had no end of trouble. A colleague and the internet has me convinced ...
2
votes
2answers
157 views

Log of Average v. Average of Log

I am constructing a dataset of monthly averages based on daily data. This dataset will be used for standard regression analysis. I anticipate wanting to transform the dependent variable, which has an ...
0
votes
1answer
42 views

Data analysis: how to compare 2 variables from each subject across 3 groups of 200 subjects?

New here and not a statistician, am MD doing research. Need advice on best method for data analysis. I have 3 groups of 200 subjects each. We collected 2 data points (A,B) from each subject. Baseline ...
1
vote
1answer
119 views

Not all positive-definite matrices are valid covariance matrices for lognormal variables

A simple method to generate correlated lognormal variables $X_i$ that obey a covariance matrix $C_{\mathrm{ln}}$ with elements $c_{\mathrm{ln}}^{ij}$ is to first compute the covariance matrix ...
1
vote
1answer
159 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 ...
0
votes
0answers
69 views

How to test whether part of the sample follows log-normal distribution?

I have a sample data that look like the following figure in a Q-Q plot with log-normal distribution. I performed an Shapiro normality test on the logarithm of the data, and reject the null hypothesis ...
1
vote
1answer
83 views

Weighting observations and measurement uncertainty in bayes

I am working on using MCMC (via STAN) to estimate model parameters for a bunch of observations with measurement uncertainty. I'm having problems with weighting each observation, and have reduced the ...
1
vote
0answers
16 views

How to reconstruct moments from aggregated data?

Let $X_{1\ldots n}$ be a stochastic variable that is log-normal distributed, with parameters $\mu$ and $\sigma$. Now suppose all $X_i$ are aggregated into $Y_{1\ldots m}$ where $Y_1$ is the mean of ...
2
votes
1answer
283 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?
3
votes
1answer
181 views

Confidence Interval of a Lognormal Random Variable

Just learning some stats, so please forgive if this is simple but I couldn't find a good explanation. Let $X \sim \mathcal{N}(\mu,\sigma^2)$ and $Y = e^X$. To find an approximately 95% confidence ...
0
votes
1answer
38 views

Lognormal distribution using normal distribution inputs

I'm simulating lognormal data in R log(Y), using the mean and standard deviation of Y. This article outlines it very well! One step in the article I'm having trouble solving how it works though. ...
5
votes
0answers
82 views

How to calculate log-normal distribution parameters with partial data?

Imagine we have a partial data and we know that this partial data represent only the left 5% of the log-normal distribution, which the overall data follow. How can we calculate the mean-log and sd-log ...
3
votes
2answers
588 views

Shifted log-normal distribution and moments

I already know how to get the moments if $X$ is log-normally distributed. But what happens when $X$ is being shifted: $Y=aX+b$, $a>0$ and $b>0$. How to compute the moments of $Y$?
3
votes
2answers
496 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 ...