1.1 KiB
1.1 KiB
MC simulations
In summary
Landau Moyal
median m_L\ex m_M\ex (μ, σ)
mode \mu_L\ex \mu_M\ex (μ)
FWHM w_L\ex w_M\ex (σ)
PDF parameters
A M(x) similar to L(x) can be found by imposing:
\vspace{15pt}
- equal mode
\mu_M\ex = \mu_L\ex \approx −0.22278298...
. . .
- equal width
w_M\ex = w_L\ex = \sigma \cdot a
\implies \sigma_M \approx 1.1191486
PDF parameters
:::: {.columns}
::: {.column width=50%}
::: {.column width=50%}
Different medians
This leads to more different medians:
\begin{align*} m_M = 0.787... \thus &m_M = 0.658... \ &m_L = 1.355... \end{align*}
Samples
- Sample
L: N = 50'000 points followingL_(x) - Sample
M: N = 50'000 points followingM_{\mu \sigma}(x)