# Source Variability

Source variability within an observation is assessed by
three methods: (1) the Kolmogorov-Smirnov (K-S)
test, (2)
the Kuiper's test, and (3) computation of
the Gregory-Loredo variability probability, all based on the source region
counts. Intra-observation source
variability within any contributing observations to a master
source entry is
assessed according to the highest level of variability seen within
any single contributing observation.
Inter-observation source
variability between any contributing observations to a master
source entry is assessed by application of a χ^{2}
hypothesis test applied to the source region photon fluxes
observed in the contributing observations.

## Properties of Individual Source Observations

#### Gregory-Loredo Variability Probability

*var_prob*

The probability that the source region flux is not uniform throughout the observation, based on the odds ratio calculated from a Gregory-Loredo analysis of the arrival times of the events within the source region. This value is calculated for each science energy band.

#### Kolmogorov-Smirnov (K-S) Test Probability

*ks_prob*

The probability that the average intervals between arrival times of events within the source region are varying and therefore inconsistent with a constant source region flux throughout the observation. The probability is computed from a one-sample, two-sided K-S test applied to the unbinned event data, with corrections applied for good time intervals and for the source region dithering across regions of variable exposure during the observation. This value is calculated for each science energy band.

#### Kuiper's Test Probability

*kp_prob*

The probability that the arrival times of the events within the source region are inconsistent with a constant source region flux throughout the observation. The probability is computed from a one-sample Kuiper's test applied to the unbinned event data, with corrections applied for good time intervals and for the source region dithering across regions of variable exposure during the observation. This value is calculated for each science energy band.

#### Variability Index

*var_index*

An index in the range [0,10] that combines (a) the Gregory-Loredo variability probability with (b) the fractions of the multi-resolution light curve output by the Gregory-Loredo analysis that are within 3σ and 5σ of the average count rate, to evaluate whether the source region flux is uniform throughout the observation. See the Gregory-Loredo Probability How and Why topic for a definition of this index value, which is calculated for each science energy band.

#### Count Rate Variability

*var_mean, var_sigma, var_min, var_max*

##### Mean Count Rate

The mean count rate (*var_mean*) is the
time-averaged source
region count rate derived from the multi-resolution light
curve output by the
Gregory-Loredo
analysis. This value is calculated for each science energy band.

##### Count Rate Standard Deviation

The count rate standard deviation
(*var_sigma*) is the time-averaged
1σ statistical variability of the source region count
rate derived from the multi-resolution light
curve output by the Gregory-Loredo analysis. This value is
calculated for each science energy band.

##### Minimum Count Rate

The minimum count rate (*var_min*) is the
minimum value of the source
region count rate derived from the multi-resolution light
curve output by the Gregory-Loredo analysis. This value is
calculated for each science energy band.

##### Maximum Count Rate

The maximum count rate (*var_max*) is the
maximum value of the source
region count rate derived from the multi-resolution light
curve output by the Gregory-Loredo analysis. This value is
calculated for each science energy band.

#### Dither Warning Flag

*dither_warning_flag*

The dither warning flag consists of a Boolean whose value is TRUE if the highest statistically significant peak in the power spectrum of the source region count rate, for the science energy band with the highest variability index, occurs either at the dither frequency of the observation or at a beat frequency of the dither frequency. Otherwise, the dither warning flag is FALSE. This value is calculated for each science energy band.

#### Gregory-Loredo Light Curve File

*see Data Products page*

Each light curve file records the multi-resolution light curve output by the Gregory-Loredo analysis of the arrival times of the source events within the source region, per observation and science energy band. A background light curve with identical time-binning to the source light curve is derived from an analysis of the events within the background region.

## Master Source Properties

### Intra-Observation:

#### Intra-Observation Gregory-Loredo, Kolmogorov-Smirnov, and Kuiper's Variability Probability

*var_intra_prob, ks_intra_prob, kp_intra_prob *

The Gregory-Loredo,
Kolmogorov-Smirnov (K-S) test, and
Kuiper's test
intra-observation
variability probabilities
represent the highest values of the variability probabilities
(*var_prob*, *ks_prob*, *kp_prob*)
calculated for each of the contributing
observations (i.e., the highest level of variability among
the observations contributing to the master source entry).

#### Intra-Observation Variability Index

*var_intra_index*

The intra-observation
variability index
(*var_intra_index*)
represents the highest value of the variability indices
(*var_index*) calculated for each of the contributing
observations.

#### Intra-Observation Count Rate Variability

*var_intra_sigma*

The intra-observation
flux variability
(*var_intra_sigma*)
is the maximum of the flux variabilities,
calculated for each of the contributing observations
by appropriately scaling the count rate variability
(*var_sigma*) in the Table of Individual
Source Observations.

### Inter-observation:

#### Inter-Observation Variability Probability

*var_inter_prob*

The inter-observation
variability probability (*var_inter_prob*)
is a value that records the probability that the source
region photon flux varied between the contributing
observations, based on the χ^{2} distribution of the
photon fluxes and the errors (standard deviation) of the individual
observations. In other words, (1 - *var_inter_prob*)
is the probability that the measured fluxes are consistent
with a non-varying source.

The reason for this careful definition is that the probabilities for intra-observation and inter-observation variability are, by necessity, of a different nature. Whereas one can say with reasonable certainty whether a source was variable during an observation covering a contiguous time interval, when comparing measured fluxes from different observations one knows nothing about the source's behavior during the intervening interval(s). Consequently, when the inter-observation variability probability is high (e.g., >0.7), one can confidently state that the source is variable on longer time scales, but when the probability is low, all one can say is that the observations are consistent with a constant flux.

#### Inter-Observation Variability Index

*var_inter_index*

The inter-observation
variability index
(*var_inter_index*)
is an integer value in the range [0,10] that is derived
from the inter-observation
variability probability
to evaluate whether the source region
photon flux is constant between the observations.
The degree of confidence in variability expressed by this index is
similar to that of the intra-observation variability index.

#### Inter-Observation Count Rate Variability

*var_inter_sigma*

The inter-observation
flux variability
(*var_inter_sigma*)
is the absolute value
of the difference between the error weighted mean source
region photon flux density of all the contributing
observations and the mean source region photon flux density
of the single observation for which the absolute value of the
difference, divided by the standard deviation for that
observation, is maximized:

Here, *i* = 1, N and N = number of contributing observations;
*<F _{ew}>* represents the

*inter*-observation error weighted mean source region photon flux density;

*<f*is the

_{i=x}>*intra*-observation mean source region photon flux density for the single observation

*x*; and

*σ*is the standard deviation corresponding to the observation

_{i=x}*x*. Of all contributing observations, observation

*x*yields the highest value for this equation, which is the value recorded by

*var_inter_sigma*.