Real Statistics Release 8.6

The new release provides the following worksheet function to perform LOESS regression.

LOESS(Rx, Ry, Rx0, npts, deg): returns a column array with the fitted values of the LOESS regression defined by Rx, Ry, and npts for the x values in Rx0.

Here we assume that Rx is a column array or range containing x data values, Ry is a column array or range with the corresponding y values, Rx0 is a column array with any number of x values, and npts = the number of points in the span.

If Rx0 is omitted it defaults to the array values in Rx. deg = 1 (default) for weighted linear regression and deg = 2 for weighted quadratic regression. If npts is omitted (or set to zero) then npts is reset to (n+deg)/3 or the next larger integer where n = the # of elements in Rx (or Ry). Rx0 can also take a scalar x value, in which case the output is the fitted y value corresponding to this x value.

For more information, see LOESS Regression using Excel.

Runs Test with more than two categories

• RUNS_TEST(s, tails) = the p-value of the runs test for the sequence defined in the string s.
• RUNS_TEST(R1, tails) = the p-value of the runs test for the sequence defined by the column or row array or range R1.
• RUNS(s) = the number of runs in string s
• RUNS(R1) = the number of runs in the row or column array or range R1.

See Runs Test with more than Two Categories for more details.

Seasonal Kendall Test

The new release supports the Seasonal Kendall Test, which determines whether there is a monotonic trend for data that has seasonality. It is essentially the Mann-Kendall test for seasonal data. The following new function is now supported:

SK_TEST(R1, per, lab, tails, alpha): returns a column array with the values test statistic, s.e., z-stat, p-value, and trend.

The arguments for this function as well as the output are the same as for the MK_TEST function except that the per argument specifies the period of seasonality (e.g. per = 4 for quarterly, per = 12 for monthly, etc.).

See Seasonal Kendall Test for more details.

• MD1X(λ, μ, lab): M/D/1 queueing model; constant (deterministic) service rate
• MG1X(λ, μ, σ, lab): M/G/1 queueing model; general service rate; σ = standard deviation of the service time
• MGinf(λ, μ, lab): M/G/∞ queueing model; general service time, infinite # of servers

Priority queueing

• MM1Pn(λ, μ, n, cum): M/M/1 queueing model
• MMsPn(λ, μ, s, n, cum): M/M/s queueing model
• MM1KPn(λ, μ, k, n, cum): M/M/1 model with a finite queue of size k
• MMsKPn(λ, μ, s, k, n, cum): M/M/s model with a finite queue of size k
• MM1NPn(λ, μ, nn, n, cum): M/M/1 model with a finite # of customers equal to n
• MMsNPn(λ, μ, s, nn, n, cum): M/M/s model with a finite # of customers equal to n
• MD1Pn(λ, μ, n, cum): M/D/1 queueing model
• MGinfPn(λ, μ, n, cum): M/G/∞ queueing model

Probability of service or queueing times

Finally, the following new worksheet functions have been added. In the following, w = the time a customer remains in the system, and w_q = the time a customer remains in the queue.

• MM1W(λ, μ, t) = P(w > t) for an M/M/1 queueing model
• MM1Wq(λ, μ, t) = P(w_q > t) for an M/M/1 queueing model
• MMsW(λ, μ, s, t) = P(w > t) for an M/M/s queueing model
• MMsWq(λ, μ, s, t) = P(w_q > t) for an M/M/s queueing model
• MD1W(λ, μ, t) = P(w > t) for an M/D/1 queueing model
• MD1Wq(λ, μ, t) = P(w_q > t) for an M/D/1 queueing model
• MM1KW(λ, μ, k, t) = P(w > t) for an M/M/1 queueing model with a finite queue of size k
• MM1KWq(λ, μ, k, t) = P(w_q > t) for an M/M/1 queueing model with a finite queue of size k
• MMsKWq(λ, μ, s, k, t) = P(w_q > t) for an M/M/s queueing model with a finite queue of size k

See Queueing Theory for more details.

Queueing Models (simulation approach)