2) Estimate the probability ([P.sub.OBS]) for the observed June 2017 precipitation in the observational data using an

empirical probability formula (Bonsai et al.

The

empirical probability of the occurrence of the events is determined as the ratio between the number of type A events that happened and the total number of observed events.

The

empirical probability model I use is simple, but flexible enough to allow for two likely non-linearities.

The model used is based on an iterative, stochastic, Monte Carlo simulation process that relies on

empirical probability distributions to generate random outputs.

For example, among all teams in major league history that ended the season with a winning percentage in the .600 bin (that is, between .590 and .610), the

empirical probability of victory when facing an opponent with winning percentage in the .400 bin (that is, between .390 and .410) is observed to be .682.

The

Empirical Probability Ratio is a measure of how similar T is with C.

Figure 4 depicts the

empirical probability density functions (pdfs) of [rho] observed in the true LoS and NLoS cases.

The CLRT and the score test statistics were performed for a variance shift model for the first observation of each simulated data and 95th percentiles from the empirical distribution of each test statistics were used as threshold values for the test statistics observed on the original data set The

empirical probability of type I errors for thresholds derived from the empirical distribution under the null hypothesis are calculated for the corrected likelihood ratio and score test statistics for [alpha] = 0.05 (Tables 1, 2, and 3).

The corresponding

empirical probability measures [[??].sub.i], i = 1, ..., K may be easily calculated from the training sets [Y.sub.i,j], where i = 1, ..., K, and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are iid observations from the distribution [P.sub.i].

Our goal in this study is to expand on this earlier work by calculating the

empirical probability of detecting lynx based on snow-track surveys in areas of known presence.

(2.) Examples include Good and Mayer (1975) and Chamberlain and Rothchild (1981); see Gelman, Katz, and Bafumi (2004) for a review of such methods and their relation to computing the

empirical probability of decisiveness.

Assumption 4, which implies that the distribution of the default time [tau] will remain the same under the

empirical probability measure P and the martingale measure Q, is required to allow the use of databases containing information about default probabilities in our empirical analysis.