  In thermal light ghost imaging, the correlation orders were usually positive
integers in previous studies. In this paper, we examine the fractional-order
moments, whose correlation order are fractional numbers, between the bucket and
reference signals in the ghost imaging system. The crucial step in theory is to
determine the precise relation between the bucket signals and reference
signals. We deduce the joint probability density function between the bucket
and reference signals by regarding the reference signals as an array of
independent stochastic variables. In calculating the fractional-order moments,
the correlation order for the reference signals must be positive to avoid
infinity. While the correlation order for the bucket signals can be positive or
negative numbers. Negative (positive) ghost images are obtained with negative
(positive) orders of the bucket signals. The visibility degree and
signal-to-noise ratio of ghost images from the fractional-order moments are
analysed. The experimental results and numerical simulations meet our analysis
based on probability theory.
