Questions tagged [lognormal]

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

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Generating random numbers that are log-normally distributed

Even though I don't quite understand why and how this works, I appreciate how simple it is to generate a set of numbers which are Poisson distributed: ...
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2 parameters to generate lognorma, but get 3 when fitting a series [closed]

I'm confused by the behavior of these two functions, used to generate a random lognormal series and fitting the same series to lognormal. When generating a lognormal series, it only gets two ...
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Is there something like z-value for log-normal distributions?

I'm looking for a reasonable way to measure how unlikely a data point is assuming it's generated by a random variable that follows log-normal. Do we have something like Z-value for normal distribution ...
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Use of Kurtosis statistic for understanding lognormality

To help clarify my understanding of this statistic, I'd appreciate feedback on the rationale presented here. Assume we have a distribution that seems potentially lognormal. Checking the median against ...
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(Regression) Confused with the distributions of fitted values, actual response values and simulated values

I have a dataset with, say, $12000$ observations, $1$ response and $10$ covariates. I want to model this dataset using a Lognormal Regression such that the mean function is given by: $E[Y\vert X]=e^{{...
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Fitting a sample streamflow data to log-normal distribution

So I'm a beginner at python and I have a streamflow data for 132 months and I need to fit every months streamflow data to lognormal distribution and finally plot the original data and fitted data on ...
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change support for dlnorm in R

I am using dlnorm() as a jumping kernel in R for a parameter with range $(0,\infty]$. However, the issue is that the range of the log-normal distribution includes ...
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Why does the log transformation bring data closer to normal distribution? [duplicate]

Quite often in published research we see researchers apply log transformation to their data, and some claim that this makes the data closer to normal distribution. My questions are: Mathematically, ...
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How to estimate parameters and pdf of a random variable transformed from a lognormal random variable?

I have a continuous random variable Y that follows lognormal distribution with known parameters (mu and sigma). Let Y be transformed to X=Y-20000. So it is basically shifted to left. How do I find the ...
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In the poweRlaw package, is the location parameter estimated for a lognormal distribution the $median=\exp(\mu)=\theta$ or $\mu$?

I have a set of graphs (each with the same nodes but with edges' weights defined by different research subjects) for which I would like to report statistics. One of these statistics is the betweenness ...
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Identifying the best distribution to this data?

I'm trying to fit an appropriate distribution to a data with 216 values and estimate parameters. From Cullen and Frey graph, it looks like lognormal could be a good fit. From q-q plot, Weibull seems ...
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Clarification of random variable with lognormal distribution (stocks)

Suppose we have a random variable $S_t$ with a log normal distribution distribution, where $S_t$ represents the price of a stock at a time $t$. Suppose that we have the annual volatility $\sigma$, of $...
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Lognormal GLM and variance estimation

I'm modeling an outcome with a positively-skewed distribution. I have chosen to use a GLM with a lognormal distribution and the identity link. Note: I am not log-transforming the outcome variable ...
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Correlation between normal and log-normal variables

(This is not a homework question.) Let $(X_1 \sim N(\mu_1,\sigma_1), X_2 \sim N(\mu_2, \sigma_2))$ be a bivariate normal random variable with the correlation between $X_1$ and $X_2$ given by $\rho$. ...
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How to calculate `mean` and `sd` of lognormal distribution based on `meanlog` and `sdlog`? [duplicate]

Lognormal distribution as below: estimate meanlog 6.0515 sdlog 0.3703 How to calculate the mean and <...
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Justification for use of non-conjugate priors?

Google searches gives no results to this question and there is the opposite question in this site, which makes me think this has an intuitive response I am missing. In most course notes and responses ...
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Mixture model for a mix of normal and lognormal distributions in R

I have a distribution composed of a mixture of a normal distribution and a log-normal distribution. A simulated example that looks quite similar to what I will expect in the real data would be: ...
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Proportional hazards model with lognormal baseline hazard in R?

I would like to fit a proportional hazards model with log normal baseline hazard in R. I have found several options for the semiparametric Cox proportional hazards, but I have not found a package to ...
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Impact of correlation bounds for Monte Carlo simulations

As the lognormal distribution imposes bounds of attainable correlations as discussed in Attainable correlations for lognormal random variables my question would be what happens if say we want to do a ...
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Lognormal distribution correlation bounds on monte carlo simulations of the minimum variance hedge ratio

As the lognormal distribution imposes bounds of attainable correlations as discussed in Attainable correlations for lognormal random variables my question would be what happens if say we want to do a ...
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Survivor function for log-normal from flexsurvreg output

I am trying to plot/generate a survival curve in Excel using the output from flexsurvreg in R. The below is a snapshot from R with the corresponding estimates (y axis values) for the time (x axis ...
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Expected value of a sum of random variables raised by $e$?

There is a function $y$ defined $$y=\exp(-\boldsymbol{\alpha}'\mathbf{b})\:\:;\:\:\:\:y\in(0,\infty)$$ where $\boldsymbol{\alpha}$ is a vector of random variables and $\mathbf{b}$ is a vector of non-...
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Undefined MGF but all moments finite?

For the lognormal distribution: https://en.wikipedia.org/wiki/Log-normal_distribution The moment generating function is undefined, but all the moments exist and are finite. I thought the moment ...
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Probability for the Quotient of two lognormal distributions (Analytical vs Monte Carlo)

I am struggling on a problem for some time now and any help would be highly appreciated. From an "easy" problem, known to have a closed-form solution, I find strange the existence of such a huge ...
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what is the distribution of the log of a normal distribution? [duplicate]

if you exponentiate a normal distribution, Y=exp{X} where X is a normally distributed random variable (RV), then Y is log-normally distributed. What is the ...
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Why do poweRlaw and fitdistrplus differ in fitted lognorm parameters

I am trying to evaluate whether a power-law fit is appropriate for some data of lake areas that we have, and whether the theoretically supported alternative of the log-normal, at least at the tails, ...
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Specifying log-normal distribution for GLM/GLMM using lme4 package

I am aware that this question has been asked before (How to specify a lognormal distribution in the glm family argument in R?) however there was no definitive answer, thus I am asking again in the ...
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How to convert log distribution to Normal Distribution

I have tried Box-Cox , exp, log etc but some features are not converting into normal distributions Please suggest me some alternative option .. As you can see in second and third graph it is not ...
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Data normalization for linear regression

I'm currently writing my thesis on the comparison of ultrasound measurements with DEXA scan measurements for specific fat distributions (40 participants). I would like to perform a linear regression ...
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Conditional Expectation given the following equations

Suppose you have a Log-Normal model with: $\log\left(x_t\right) = \mu_t + \varepsilon_t$ $\mu_{t+1} = \mu_t + \delta_t$ $\delta_{t+1} = \delta_t + \gamma_t$ where $\varepsilon_t \sim \text{NID}\...
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Fitting lognormal distribution from D10, D50, and D90 [duplicate]

I have a statistical sample where D10 = 8 (10% of population under the value 8), D50 = 11 (median), and D90 = 18 (90% of population under the value 18) Now, I need to find the best fit, in terms of ...
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Determine Normal Distribution based on LogNormal Distribution

Suppose that we have that $Y=e^{aX}$ where $a$ is a positive scalar. We know that $Y$ follows a logNormal distribution with parameters $0$ and $2$. Then is there a way to derive the distribution of $X$...
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Determining average duration between input and output (example - CoVID-19 sickness)

Let us assume there are given two sets on data, input and output of a process. For an example, daily number of infected people by CoVID-19 and daily number of resolved cases, be it death or healing. ...
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In a lognormal distribution, is the median further left than when the variable is logged?

I created a kernel density estimate of the earnings distribution in South Africa in 2017, quarter 4, using Stata. I summarized the earnings variable, putting a sampling weight as an analytical weight ...
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Higher moments of Lognormal Distribution

I am experiencing a weird problem modeling lognormal distributions and I am quite stuck on this one. For a normal distributed variable X following a $N(\mu,\sigma^2)$ distribution, we have that $Z=e^...
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Interpreting truncated normal and lognormal coefficients

I am running a truncated normal regression and a lognormal regression as the second part of a double hurdle model. The dependent variable is transaction revenue and I have several independent ...
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How can I make a probability paper plot of a log-normally distributed variable?

My company has software that can take a vector of samples and easily create a probability plot of the data and the least-squares or method of moments fit of the data. However, I need to be able to ...
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One-way ANOVA or Kruskal Wallis in SPSS for non-normal data that shows no homogeneity of variance?

I have fisheries catch data that I need to analyse for my thesis. I already did meta-analysis in Excel, and got some main trends and percentiles out of it. For other stats I am using SPSS. I was ...
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Comparing Discrete Lognormal Distributions

Is it possible to have the following: Create an approximation of the discrete lognormal distribution? Given a discrete distribution in the form of a histogram, is it possible to compare its ...
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Let 𝑋 be a Log-Normally distributed RV with 𝜇 = 3 and 𝜎 = 2. Determine 𝐸[max(𝑋 − 100, 0)]

See the question above. I am not quite sure, if my result is correct, because I do not have any solutions. I tried with the following formula: $$ E[X] = e^{\mu+\frac{1}{2} \sigma^{2}} \cdot \Phi\left(...
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Let 𝑋 be a Log-Normally distributed RV with 𝜇 = 3 and 𝜎 = 2. Determine 𝑃 (100 ≤ 𝑋 ≤ 150)

I do not get how $\Phi\left(\frac{\ln (100)-3}{2}\right)$ and $\Phi\left(\frac{\ln (150)-3}{2}\right)$ should give me the probabilities 0.7889 and 0.8426 respectively. I looked at the distribution ...
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How to interpret a Log Normal Distribution

I have a dataset with 3 columns that are found out to be log-normally distributed. I am a little bit confused about how can I draw the conclusion in a log-normal distribution similar to Normal ...
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Should I use log transformed pharmacokinetic data or use GLM gamma regression with log link?

I was taught, that when we deal with data of multiplicative nature, following the log-normal distribution, like in pharmacokinetic analyses, we should log the data first to enable classic parametric ...
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1answer
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Appropriate to fit lognormal model to data with heavy tail?

I am attempting to standardize recreational fishery CPUE data. I am using a delta approach, with a binomial model fit to the presence/absence data and a lognormal model fit to the positive ...
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What is the full-conditional distribution for $log(\sigma) \sim N(\mu_\sigma,\tau_\sigma^2)$?

What is the full-conditional distribution for $[\sigma|\textbf{y},\mu]$ given the following hierarchical structure?: $y_i \sim N(\mu,\sigma^2)$ $\mu \sim N(\mu_0, \sigma^2_0)$ $log(\sigma) \sim N(\...
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How to derive CDF of lognormal distribution? [duplicate]

Can someone explain how I can derive CDF for lognormal distribution from this PDF: $$f(t)=\frac1{\sqrt{2\pi}}\gamma t^{-1}e^{-\gamma^2(\log(\lambda t))^2/2}$$ I need this CDF function for Survival ...
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1answer
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How is that possible that simple arithmetic mean works well even for strongly skewed distribution?

I was taught, that the arithmetic mean is sensitive to outliers and skewness. This was natural to me - the observations lying far from the "central point" of the distribution "pull" the measure ...
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Why summarise right-skewed distributed (log-normal) data with geometric mean rather than its expected value?

I am very confused. The first raw moment calculated from sample, the arithmetic mean, is the BLUE estimator of its expected value. So there is no better one. At the same time, I was told that the ...
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Deriving the un-normalized log posterior on sigma

Hello I'm trying to derive the un-normalized log posterior on sigma this is what I have so far $$ p \left(\sigma \mid \mathbf{x}, \mu\right) \propto \log \left( p \left(\sigma \mid \mathbf{x}, \mu\...
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1answer
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Question about the decision between normal and lognormal distribution in a linear model

I hope someone could help me with the following problem: If I create a linear model that predicts the height of people (y) with the following parameters: y = a + b*(xi-xavg) with "a" the normally ...

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