MSPRT (version 2.1)

ovr.repl.oneZ: A particular replication step in overshoot.oneZ()

Description

In one-sample Z-tests this function simulates a data, computes the likelihood ratios, and compares with the acceptance and rejection thresholds. overshoot.oneZ() carries out a Monte Carlo method by repeating this function for R number of times.

Usage

ovr.repl.oneZ(error.type, batch.seq, null, gen.par, alt.LR, up, low, N, seed)

Arguments

error.type

a character; specifies which of the 2 types of errors need to be accounted for.

"type1" for Type 1 error.

"type2" for Type 2 error.

batch.seq

a numeric vector; an increasing sequence of values until N. Denotes the sequence of sample sizes where a user will observe data sequentially.

Last element should equal to N.

null

a numeric; the hypothesized value of population mean under the simple null hypothesis.

gen.par

a numeric vector of length 2; the first component is the value of the population mean and second component is the known standard deviation (sd).

Observations are generated from a normal distribution with this mean and sd.

alt.LR

a numeric; the simple alternative in favor of which the likelihood ratios (\(L_n\)) are calculated sequentially.

The UMPBT point alternative is used in case of a MSPRT. This is same with the output u from umpbt.oneZ().

up

a numeric; value of a constant rejection threshold; should be greater than low.

low

a numeric; value of a constant acceptance threshold; should be smaller than up.

N

a positive numeric (integer); number of samples where truncation of Wald's SPRT is required;

in a MSPRT, this is the maximum available sample size.

seed

a positive integer; used in set.seed() to recreate the simulated data.

Value

Returns a list with following components:

incr.count

either 0 or 1; 1 if and only if an error of error.type is made.

inconclusive

a numeric; the value of \(L_N\) if and only if it remains inconclusive after truncating Wald's SPRT at N; otherwise a numeric of length 0 is returned.

n

a numeric; number of samples required for reaching the decision. In an inconclusive case, this value is N.

References

Wald, A., Sequential Tests of Statistical Hypotheses. Ann. of Math. Statist., vol. 16, no. 2, 1945, 117-186.

Examples

# NOT RUN {
N.max = 30
ovr.repl.oneZ( error.type= "type1", batch.seq= 1:N.max, null= 0,
               gen.par= c(0,1), alt.LR= 1, up= 160, low= 0.2, 
               N= N.max, seed= 1)

ovr.repl.oneZ( error.type= "type2", batch.seq= 1:N.max, null= 0,
               gen.par= c(1.5,1), alt.LR= 1, up= 160, low= 0.2, 
               N= N.max, seed= 1)

# }