1.3 KiB
1.3 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)
Moyal 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...
Moyal parameters
:::: {.columns}
::: {.column width=50%}
::: {.column width=50%}
Moyal parameters
This leads to more different medians:
\begin{align*} m_M = 0.787... \thus &m_M = 0.658... \ &m_L = 1.355... \end{align*}
Compatibility test
Comparing results:
p = 1 - \text{erf} \left( \frac{t}{\sqrt{2}} \right)\ \with
t = \frac{|x\ex - x\ob|}{\sqrt{\sigma\ex^2 + \sigma\ob^2}}
x\exandx\obare the expected and observed values\sigma\exand\sigma\obare their absolute errors
. . .
At 95% confidence level, the values are compatible if:
p > 0.05