Solar Phys (2014) 289:193–209 DOI 10.1007/s11207-013-0334-4 Statistical Moments of Active-Region Images During Solar Flares S. Šimberová · M. Karlický · T. Suk Received: 27 August 2012 / Accepted: 20 May 2013 / Published online: 20 July 2013 © Springer Science+Business Media Dordrecht 2013 Abstract We present new temporal-evolution diagnostics of solar flares. The high-order statistical moments (skewness and kurtosis) of the Hα images of active regions during solar flares were computed from their initial phases up to their maxima. The same method was used for quiet active regions for tests and comparison. We found that temporal profiles of the Hα statistical moments during flares roughly correspond to those observed in soft X-rays by the GOES satellite. Maxima of the cross-correlation coefficients between the skewness and the GOES X-rays were found to be 0.82 – 0.98, and the GOES X-rays are delayed 0 – 144 seconds against the skewness. We recognized that these moments are very sensi- tive to pre-flare activities. Therefore we used them to determine the flare starting-time and to study the pre-flare quasi-periodic processes. We determined the periods of these pre-flare processes in an interval of 20 – 400 seconds by using special convolution filters and Fourier analysis. We propose to use this method to analyze active regions during the very early phases of solar flares, and even in real time. Keywords Sun: solar flares · Moments · Frequency analysis · Pattern recognition 1. Introduction There are various processing methods for analyzing solar active regions. The processing algorithms are designed for data observed by ground-based or satellite instruments consid- ering the wavelength, time sequence, sampling frequency, temporal and spatial resolution, S. Šimberová ( ) · M. Karlický Astronomical Institute, Academy of Sciences of the Czech Republic, Ondˇ rejov 251 65, Czech Republic e-mail: ssimbero@asu.cas.cz M. Karlický e-mail: karlicky@asu.cas.cz T. Suk Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague 8, 182 08, Czech Republic e-mail: suk@utia.cas.cz