# a.estimate: Estimate the Left Endpoint of the Off-Pulse Interval of a... In SOPIE: Non-Parametric Estimation of the Off-Pulse Interval of a Pulsar

 a.estimate R Documentation

## Estimate the Left Endpoint of the Off-Pulse Interval of a Pulsar

### Description

a.estimate and b.estimate is almost identical function. a.estimate is the function used to obtain the estimated values of a, i.e. \hat a, for the off-pulse interval of a pulsar light curve. b.estimate is the function used to obtain the estimated values of b, i.e. \hat b, for the off-pulse interval of a pulsar light curve.

### Usage

a.estimate(data, to = 1, min_points, alpha = 0.05, g = 1, r = 1)


### Arguments

 data  the data vector used to estimate a. to  the value of the maximum domain of the data. Values will usually either be 1 or 2π. min_points  the scalar or vector containing the value(s) of the minimum point(s) calculated during the kernel density estimation. This argument does not represent the index value(s) of the observations within data. The minimum point(s) can be obtained with the function circ.kernel. alpha  significance level (α) that will be used during the sequential application of the goodness-of-fit tests for uniformity when estimating the off-pulse interval. g  the value of the incremental growth of each subsequent interval over which uniformity is tested. In the suggested procedure, uniformity is sequentially tested, with the interval used in the test growing by g observations after every iteration. The selection of g not only influences the computation time of the procedure, but also has an effect on the point where rejection of the hypothesis takes place. For large values of g, the user takes the risk that uniformity is rejected for a certain (larger) interval, while it should have been rejected earlier (for a smaller interval). On the other hand, a very small choice of g results in long execution times. Small values of g may also result in the early rejection of uniformity, e.g. in the situation where a few observations may cause the rejection of uniformity, while uniformity is again confirmed when several more observations are included in the interval. If the user suspects that this situation may occur, the problem can be overcome by selecting a larger value of the integer r. r  the number of subsequent intervals that must result in the rejection of uniformity before the function will stop. The choice of r must therefore be linked to the choice of g as explained above. For smaller values of g, it would be safer to select larger values of r, and vice versa. Since small values of g may result in a temporary rejection of uniformity for an interval, a larger value of r would prevent the method from immediately stopping at the first occurrence of rejection. It is very important to note that, for a large value of r, there will be no impact on the value of \hat b or \hat a if rejection takes place for each interval after a certain point.

### Value

a list containing the following components:

 summary  a vector containing the estimated value of a, i.e. \hat a, for each of the four goodness-of-fit tests, namely the Anderson-Darling, Kolmogorov-Smirnov, Cramer-von Mises and the Rayleigh goodness-of-fit test. general  a list containing the function call, the minimum value(s) used in the estimation, the level of significance (α), the value of g and the value of r.

### Author(s)

Willem Daniel Schutte

### References

D'Agostino, R. & Stephens, M. (eds) (1986). Goodness-of-t techniques, Marcel Dekker, Inc.
Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, World Scientific Publishing Co. Pte. Ltd.
Marsaglia G, Marsaglia J (2004). Evaluating the Anderson-Darling Distribution. Journal of Statistical software, 9, 1-5.
Marsaglia G, Tsang WW, Wang J (2003). Evaluating Kolmogorov's Distribution. Journal of Statistical Software, 8(18), 1-4.
Schutte WD, Swanepoel JWH (2016). SOPIE: an R package for the non-parametric estimation of the off-pulse interval of a pulsar light curve. Monthly Notices of the Royal Astronomical Society, 461, 627-640.
Stephens M (1970). Use of the Kolmogorov-Smirnov, Cramer-Von Mises and related statistics without extensive tables. Journal of the Royal Statistical Society. Series B (Methodological), 32, 115-122.

ad.test , ks.test , rayleigh.test

### Examples

## This function is to be used inside the wrapper function SOPIE

simdata<-von_mises_sim(n=5000,k=1,c=0.3,noise=0.2)
SOPIE(simdata,h=1,to=1,alpha=0.05,g=5,r=10,m=1,grid=100)


SOPIE documentation built on March 18, 2022, 5:25 p.m.