Calculates the probability of a management value exceeding a reference point with or without error

`pgen(est=NULL,limit=NULL,estSD=0,limSD=0,corr=0,dist=1,comp=1,nreps=10000)`

est

management value (mv) or vector containing individual parameter values from, say, bootstrap runs.

limit

reference point (rp) or vector containing individual reference point values from, say, bootstrap runs.

estSD

standard deviation of management value if a single value is used. Must be >0 if a single value is used. If a vector of individual values is provided, estSD is not used.

limSD

standard deviation of reference point if a single value is used. If a vector of individual values is provided, limSD is not used. limSD = 0 if the reference point is considered a point estimate (no error).

corr

correlation between est and limit. Only used if est and limit are single values with error.

dist

assumed distribution of est or limit if they are single values with error. 1 = normal; 2 = log-normal.

comp

the direction of comparison: 1: mv < rp, 2: mv <= rp, 3: mv > rp, 4: mv >= rp.

nreps

the number of samples to draw to create normal or log-normal distributions. User should explore different sample sizes to determine if the probability obtained is stable.

probability value of comparison

Randomization methods as approximations to Equations 1, 2 and 3 in Shertzer et al. (2008) are used to calculate the probability that a management value with error (e.g., fishing mortality) passes a reference point without (Eq. 1) or with (Eq. 2) error. Either may be represented by a single value and its associated standard deviations or a vector of individual values that represent results from, say, bootstrap runs. If log-normal is assumed, mv and rp and associated standard deviations must be in natural log-units (i.e., meanlog and sdlog).

If the management value and reference point are specified as single values with standard deviations,
samples of size *nreps* are drawn randomly from the specified distribution parameterized with
*est* and *limit* and associated standard deviations. If *corr*>0 (Eq. 3), then the *est* and
*limit* distributions are drawn from a multivariate normal (function *mvrnorm*) distribution. If log-normal
is assumed, function *mvrnorm* is used with the meanlog and sdlog estimates and then output values are
bias-corrected and back-transformed.

If the management value and the reference point are represented by vectors of individual values,
the probability is calculated by tallying the number of management values that exceed (or pass) the
reference points and then dividing by number of est values*number of limit values. If either the management value
or reference point is specified as a single value with standard deviation, then a vector of individual values of
size equal to the size of the other vector is generated by using the *rnorm* or *rlnorm* function
parameterized with the single value and its standard deviation.

Shertzer, K. W., M. H. Prager, and E. K. Williams. 2008. A probability-based approach to setting annual catch levels. Fishery Bulletion 106: 225-232.

```
# NOT RUN {
## est = 2010 Spawning Stock Biomass of Striped Bass, limit = SSB Reference Point
pgen(est=50548,limit=36881,estSD=5485,limSD=1901,corr=0.05,dist=1,comp=2,nreps=1000)
# }
```

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