Questions tagged [lognormal-distribution]
A lognormal distribution is the distribution of a random variable whose logarithm has a normal distribution.
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Comparing Gaussian GLMM models for positive, slightly non-normal data: Interpreting conflicting model selection criteria
I'm analyzing data using glmmTMB in R with the following model structure:
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In a sum of high-variance lognormals, what fraction comes from the first term?
If $X_i \overset{\textrm{iid}}{\sim} \text{Lognormal}(0, \sigma^2)$ for $i=1,\ldots,n$ and $Y_1 = X_1 / \sum_{j=1}^n X_j$, then I would expect that a particular* limiting distribution of $Y_1$, ...
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Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript
I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution.
I think a fairly intuitive way for a lay person to ...
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Delta method vs actual expectation
If $x \sim N(\mu,\sigma^2)$, then by first principles,
$$\mathbb{E}(e^x) = e^{\mu + \sigma^2 / 2}.$$
I am trying to figure out where the "Delta method" is wrong here: If $(x-\mu) \sim N(0,\...
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Autocorrelation of the lognormal Black-Scholes process
The Black-Scholes model with constant volatility $\sigma$ and interest rate $r$ is defined as
$$
dS_t/S_t=rdt+\sigma dW_t
$$
I derived the autocorrelation of the spot process $S_t$ for future times $0&...
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Transformed Ornstein Uhlenbeck process
Say I have 𝑋 that follows an Ornstein-Uhlenbeck process:
$𝑑𝑋_𝑡=𝜙X_t𝑑𝑡+𝜎𝑑𝑊_𝑡$
Let $𝑌_𝑡=exp(𝑋_𝑡)$.
How can I calculate the autocorrelation function of $Y_t$?
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How do you determine an appropriate block length for calculating "block maxima" for GEV distribution?
I have some time series data spanning 30+ years and I am trying to do some extreme value analysis. Major disclaimer: I am not a statistician so I feel that I am wading into waters beyond my area of ...
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When to calculate the bias corrected geometric mean
Most sources give a simple equation to compute the geometric mean (GeoMean) of data samples from a lognormal distribution.
GeoMean = exp(m)
where m is the mean of ...
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Interpreting AFT Model Coefficients: Mean vs. Median Survival Time in Log-Normal Distribution
When interpreting the coefficients of an Accelerated Failure Time (AFT) model that assumes a log-normal distribution, should we focus on the impact of coefficients on the mean survival time or the ...
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compare means of lognormal distribution
I have a small set of data that I used to generated a lognormal distribution:
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Using simulations to prove E[Y] formula of a log normal distribution [duplicate]
Assume that $X∼ N (μ, σ^2)$ and that $Y = e^X$ and we have set $μ = 0$ and $σ = 1.5$. We have to prove that $E[Y] = e^{(μ+σ^2)/2}$ using 10000 simulations. I.e. ...
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Is it possible to fit a linear model of y in log scale but with offset in the original scale?
Let's start with simple linear regression with log transformation of the response variable y:
$$ \log(y_i) = \beta_0 + \beta_1x_i + e_i$$
(btw, how is this model called? log-linear regression or ...
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Expected value of the square root of a lognormal variable
Let $X$ be a positive, lognormal random variable with known mean $\mu_X$ and variance $\sigma_X^2$. Since $X$ is a lognormal random variable, I know its pdf and moment-generating function (mgf).
pdf:
$...
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Numerical moments of a multivariate Poisson Log-normal posterior
I have a log-density of the form:
$$P(\mathbf{x}) \propto \exp\left( - \mathbf{b}^{\top} e^{ \mathbf{x} } - \frac{1}{2}\mathbf{x}^{\top}A\mathbf{x} \right)$$
where $A$ is a symmetric positive definite ...
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Suppose I am using KM curve to estimate S(t) parametrically (say assuming it follows lognormal)
Suppose I am using KM curve to estimate S(t) parametrically (say assuming it follows lognormal). Now this t is in (say) months, and I want to get estimates of the lognormal curve where t is in weeks, ...
