Return to Answer

Depending on your needs, some characteristics per sample ($\times 10^n$ as appropriate) of simulated $f$ (plus the CDF, $F=\int f$, and quantile function $F^{-1}$) that may be of interest for procedure 1 vs procedure 2:

• Computational time

• Memory cost

• Energy cost

• Uniformity of $p$ (from $F^{-1}$)

• Accuracy in the tails of $f$

• Accuracy for the distribution overall from an analytic formulation of $f$ (e.g., using a one-sample Kolmogorov-Smirnof test for each procedure for many samples of size $N$ and comparing the mean $p$ values).

The particular statistics tracked from simulating a univariate distribution will necessarily depend on the purposes envisioned for using it. For example, if the number of needed simulations is anticipated to be on the order of, say, $10^6$ per day or less, then you may not need to calculate compute time, memory, or energy costs. However, if anticipated need for simulated draws from $f$ is at a much greater rate, say $10^9$ per hour or more, then those costs per sample may be relevant.

Depending on your needs, some characteristics per sample ($\times 10^n$ as appropriate) of simulated $f$ (plus the CDF, $F=\int f$, and quantile function $F^{-1}$) that may be of interest for procedure 1 vs procedure 2:

• Computational time (e.g., measured using clock cycles, seconds, or represented analytically using big O notation)

• Memory cost

• Energy cost

• Uniformity of $p$ (from $F^{-1}$)

• Accuracy in the tails of $f$

• Accuracy for the distribution overall from an analytic formulation of $f$ (e.g., using a one-sample Kolmogorov-Smirnof test for each procedure for many samples of size $N$ and comparing the mean $p$ values).

The particular statistics tracked from simulating a univariate distribution will necessarily depend on the purposes envisioned for using it. For example, if the number of needed simulations is anticipated to be on the order of, say, $10^6$ per day or less, then you may not need to calculate compute time, memory, or energy costs. However, if anticipated need for simulated draws from $f$ is at a much greater rate, say $10^9$ per hour or more, then those costs per sample may be relevant.

Depending on your needs, some characteristics per sample ($\times 10^n$ as appropriate) of simulated $f$ (plus the CDF, $F=\int f$, and quantile function $F^{-1}$) that may be of interest for procedure 1 vs procedure 2:

• Computational time

• Memory cost

• Energy cost

• Uniformity of $p$ (from $F^{-1}$)

• Accuracy in the tails of $f$

• Accuracy for the distribution overall from an analytic formulation of $f$ (e.g., using a univariate Kolmogorov-Smirnof test)

The particular statistics tracked from simulating a univariate distribution will necessarily depend on the purposes envisioned for using it. For example, if the number of needed simulations is anticipated to be on the order of, say, $10^6$ per day or less, then you may not need to calculate compute time, memory, or energy costs. However, if anticipated need for simulated draws from $f$ is at a much greater rate, say $10^9$ per hour or more, then those costs per sample may be relevant.

Depending on your needs, some characteristics per sample ($\times 10^n$ as appropriate) of simulated $f$ (plus the CDF, $F=\int f$, and quantile function $F^{-1}$) that may be of interest for procedure 1 vs procedure 2:

• Computational time

• Memory cost

• Energy cost

• Uniformity of $p$ (from $F^{-1}$)

• Accuracy in the tails of $f$

• Accuracy for the distribution overall from an analytic formulation of $f$ (e.g., using a one-sample Kolmogorov-Smirnof test for each procedure for many samples of size $N$ and comparing the mean $p$ values).

The particular statistics tracked from simulating a univariate distribution will necessarily depend on the purposes envisioned for using it. For example, if the number of needed simulations is anticipated to be on the order of, say, $10^6$ per day or less, then you may not need to calculate compute time, memory, or energy costs. However, if anticipated need for simulated draws from $f$ is at a much greater rate, say $10^9$ per hour or more, then those costs per sample may be relevant.

Depending on your needs, some characteristics per sample ($\times 10^n$ as appropriate) of simulated $f$ (plus the CDF, $F=\int f$, and quantile function $F^{-1}$) that may be of interest for procedure 1 vs procedure 2:

• Computational time

• Memory cost

• Energy cost

• Uniformity of $p$ (from $F^{-1}$)

• Accuracy in the tails of $f$

• Accuracy for the distribution overall (e.g., using a univariate Kolmogorov-Smirnof test)

The particular statistics tracked from simulating a univariate distribution will necessarily depend on the purposes envisioned for using it. For example, if the number of needed simulations is anticipated to be on the order of, say, $10^6$ per day or less, then you may not need to calculate compute time, memory, or energy costs. However, if anticipated need for simulated draws from $f$ is at a much greater rate, say $10^9$ per hour or more, then those costs per sample may be relevant.

Depending on your needs, some characteristics per sample ($\times 10^n$ as appropriate) of simulated $f$ (plus the CDF, $F=\int f$, and quantile function $F^{-1}$) that may be of interest for procedure 1 vs procedure 2:

• Computational time

• Memory cost

• Energy cost

• Uniformity of $p$ (from $F^{-1}$)

• Accuracy in the tails of $f$

• Accuracy for the distribution overall from an analytic formulation of $f$ (e.g., using a univariate Kolmogorov-Smirnof test)

The particular statistics tracked from simulating a univariate distribution will necessarily depend on the purposes envisioned for using it. For example, if the number of needed simulations is anticipated to be on the order of, say, $10^6$ per day or less, then you may not need to calculate compute time, memory, or energy costs. However, if anticipated need for simulated draws from $f$ is at a much greater rate, say $10^9$ per hour or more, then those costs per sample may be relevant.