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

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Fitting Claims Data [on hold]

I am trying to fit claims data using extreme value analysis. I have claims data and want to find a threshold value and fit a lognormal dist on the body and a GPD on the tail using R and to measure ...
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1answer
21 views

Hierarchical Bayesian model - issues with JAGS/BUGS switching between lognormal and normal

I'm trying to construct a hierarchical model using JAGS, but I'm running into issues converting between normal/lognormal distributions and the more I stare at my problem, the more confused I get. ...
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12 views

How do I fit a set of data that has a lower and upper bound to a lognormal distribution in R?

I have data only above 200,000 and up to 1,000,000, is there a simple R command that will permit me to fit a lognormal distribution to this data? Same for a pareto distribution?
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13 views

Comparison of Scale Parameters

I have several lognormal models, created from reliability data set and I was wondering if there is a way (like Tukey, Scheffe) to compare the scale parameters, to see if they share a common parameter. ...
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14 views

Cross correlation of gaussian signals with its mean signal gives non-gaussian distributed scores

The following is my question: I have signals that contains noise, they are of the following form see the figure below.. Then I take the mean signal of all these signals (identical in length and ...
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28 views

sample size to estimate mean of zero modified log normal variable

I would like to estimate the average value of a variable "A" in a population. I think only 5% of the population has a figure of A > 0, 95% has A = 0. Using a previous non random sample, I believe the ...
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60 views

What's the story behind the log-normal distribution?

I have been playing around with datasets for the past while for practice. I've noticed that a distribution that looks something like the following appears: This shape appears frequently! I can ...
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36 views

Jointly Sufficient Statistic Question

So here is a problem I have been working on: Suppose that survival time $X$ has a lognormal distribution with parameters $\mu$ and $\theta$ (which are the mean and standard deviation of $\log(X)$, not ...
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1answer
16 views

Generate Example data for which it is difficult to distinguish between Gamma, Weibull and log-normal fit using R?

I'm trying to generate a data set, as a demonstration case, to show a case in which it is difficult to distinguish between Gamma, Weibull and log-normal distribution. To do this I generate some data: ...
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17 views

Difference between gaussian and lognormal

I have to study tolerance intervals for a distribution of a random variable Z that is given by the difference of a normal X minus a (independent) lognormal Y. To begin with I tried to get an ...
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29 views

R timeseries data thats not normally distributed

I have time series data set in R that is skewed to the left, before I try and work with it should I be trying to "normalize" it IE x1ts is skewed x1tsNORM <- log(x1ts) will this make future ...
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1answer
72 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 ...
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53 views

Why is this Bayesian estimate of a truncation-point so poor?

I have several datasets. Each dataset holds the masses of objects that have been subject to physical wear, expressed as a proportion of their original mass ($w$), and the amount of time that the ...
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0answers
19 views

zipf and correlated lognormal

I have been struggling with this for a while. I want to generate two random variables $X$ and $Y$ with a particular correlation $\rho$ where $X$ is the file popularity (zipf distribution) and $Y$ is ...
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1answer
25 views

Skewness of log-normal distribution only depending on variance?

Wikipedia says that the skewness of the log-normal distribution only depends on the variance of the underlying normal distribution. Skewness: However, from my point of view the skewness increases ...
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3answers
96 views

Interpreting Standard Deviation of Natural Log Transformed Data

I am interested in interpreting (back transforming) the effect of a one standard deviation (sd) increase in a log transformed on the non-transformed variable. So let's say I have a variable Y: ...
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9 views

Under which conditions two lognormal distributions l1, l2 have median(l1+l2) = median(l1)+median(l2)?

are there any conditions on two lognormal l1 and l2 RVs which satisfy: median(l1+l2) = median(l1) + median(l2) They can be correlated and/ or dependent. In case the answer is affirmative, is it ...
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28 views

Transformation of data with zero and R squared

I have a conceptual concern about data tranformation and R^2. Often we transform data to respect the assumption of the linear model. Therefore, we can use multiple type of transformation such as log ...
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1answer
38 views

lognormal distribution average and variance

I am trying to get acquainted with this type of distribution, and part of it is exploring what random number generation with scipy.stats produces. I have noticed ...
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0answers
28 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 ...
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21 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 ...
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2answers
176 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 ...
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1answer
105 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 ...
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1answer
52 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): ...
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66 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? ...
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1answer
39 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 ...
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1answer
82 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 ...
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1answer
105 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. ...
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1answer
62 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 ...
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1answer
113 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 ?
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82 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 ...
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18 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, ...
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23 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 ...
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1answer
152 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 ...
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60 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 ...
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1answer
85 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 ...
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1answer
65 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 ...
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1answer
256 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 ...
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22 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 ...
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1answer
691 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 ...
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1answer
61 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 ...
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1answer
72 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 ...
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67 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. ...
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1answer
113 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 ...
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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 ...
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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 ...
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1answer
83 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 ...
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0answers
38 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 ...
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1answer
46 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 = ...
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137 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 ...