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The study concentrated on the fractal dimension of solar activity and climatic parameters. We analyzed comparatively for each parameter numerically. All values are estimated by Box Counting technique of fractal dimension. According to the theme of study, we used a monthly dataset of Coronal Mass Ejection (Coronal Index (CI)), ElNino Southern Oscillation (ENSO) and Quasi-Biennial Oscillation (QBO) from 1954 to 2016. The time seriesof ENSO and QBO are distributed according to the CORONAL INDEX (CI) cycles (19, 20, 21, 22, 23, and 24) to understand their relationship in the perspective of persistence or anti-persistence.The fractal dimension(D) represents the complexity and Hurst exponent(H) indicates the long memory dependence of the selected time series, with scaling constant (a, c). The results obtained indicate the persistence (1 < D < 1.5) for CORONAL INDEX (CI) with distributed ENSO and QBO cycles. The fractional Brownian motion (fBm) is also found long memory dependence(1¿H¿ 0.5) and locally lowpass signal for all studied cycles observed.A linear relationship implies between Hurst coefficient and fractal dimension for a statistical assumption (H + D = 2).The fractal scaling instrument is established between the global indices (ENSO & QBO) and solar activity (particularly CORONAL INDEX (CI)) cycles,the inverse correlation with ENSO and direct with QBO are observed. The results obtained in this research work may help to describe the solar-terrestrial relationship

The research work done in this paper comprises the application of different well-known probability distribution models. This includes the understanding of the behavior and dynamics of 24 sunspot cycles with total data. The time-series data sets were selected from 1749 to 2014. To observe the solar activity effects on K-index activity the double cycles from 1932 to 2014 were also incorporated in the study. The comparative study is useful to observe the long-term solar-terrestrial connection. The magnetic field of the sun reverses its polarity after every 11 years of the cycle. So after every 22 years, the north pole becomes again north pole. By using the two well-known tests Kolmogorov-Smirnov (KST) and Anderson-Darling test (ADT) the probability distribution models were obtained for each sunspot cycles and compare. The significant probability models for all the sunspot cycles have been obtained. The fitted probability distribution models on selected data sets may be useful to understand the trend of solar and geomagnetic activity.