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We carry out a study of the statistical distribution of rainfall precipitation data for various cites in India, motivated by similar work done in Ghosh et al (2016), which studied the probability distribution of rainfall in multiple cities in Bangladesh. We have determined the best-fit probability distribution for the monthly precipitation data spanning 100 years of data from 1901 to 2002, for multiple stations located all over India, such as Gandhinagar, Guntur, Hyderabad, Jaipur, Kohima, Kurnool, and Patna. To fit the observed data, we considered the Fisher, Gamma, Gumbel, Inverse Gaussian, Normal, Weibull, Student-t, Beta, and Generalized Extreme Value distributions. The efficacy of the fits for these distributions are evaluated using four empirical non-parametric goodness-of-fit tests namely Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Chi-Square, Akaike information criterion(AIC) and Bayesian Information criterion (BIC). Finally, the best-fit distribution using each of these tests are reported for the various cities.

We carry out a study of the statistical distribution of rainfall precipitation data for various cites in India, motivated by similar work done in Ghosh et al (2016), which studied the probability distribution of rainfall in multiple cities in Bangladesh. We have determined the best-fit probability distribution for the monthly precipitation data spanning 100 years of data from 1901 to 2002, for multiple stations located all over India, such as Gandhinagar, Guntur, Hyderabad, Jaipur, Kohima, Kurnool, and Patna. To fit the observed data, we considered the Fisher, Gamma, Gumbel, Inverse Gaussian, Normal, Weibull, Student-t, Beta, and Generalized Extreme Value distributions. The efficacy of the fits for these distributions are evaluated using four empirical non-parametric goodness-of-fit tests namely Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Chi-Square, Akaike information criterion(AIC) and Bayesian Information criterion (BIC). Finally, the best-fit distribution using each of these tests are reported for the various cities.

We carry out a study of the statistical distribution of rainfall precipitation data for various cites in India, motivated by similar work done in Ghosh et al (2016), which studied the probability distribution of rainfall in multiple cities in Bangladesh. We have determined the best-fit probability distribution for the monthly precipitation data spanning 100 years of data from 1901 to 2002, for multiple stations located all over India, such as Gandhinagar, Guntur, Hyderabad, Jaipur, Kohima, Kurnool, and Patna. To fit the observed data, we considered the Fisher, Gamma, Gumbel, Inverse Gaussian, Normal, Weibull, Student-t, Beta, and Generalized Extreme Value distributions. The efficacy of the fits for these distributions are evaluated using four empirical non-parametric goodness-of-fit tests namely Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Chi-Square, Akaike information criterion(AIC) and Bayesian Information criterion (BIC). Finally, the best-fit distribution using each of these tests are reported for the various cities.

We carry out a study of the statistical distribution of rainfall precipitation data for various cites in India, motivated by similar work done in Ghosh et al (2016), which studied the probability distribution of rainfall in multiple cities in Bangladesh. We have determined the best-fit probability distribution for the monthly precipitation data spanning 100 years of data from 1901 to 2002, for multiple stations located all over India, such as Gandhinagar, Guntur, Hyderabad, Jaipur, Kohima, Kurnool, and Patna. To fit the observed data, we considered the Fisher, Gamma, Gumbel, Inverse Gaussian, Normal, Weibull, Student-t, Beta, and Generalized Extreme Value distributions. The efficacy of the fits for these distributions are evaluated using four empirical non-parametric goodness-of-fit tests namely Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Chi-Square, Akaike information criterion(AIC) and Bayesian Information criterion (BIC). Finally, the best-fit distribution using each of these tests are reported for the various cities.

We carry out a study of the statistical distribution of rainfall precipitation data for various cites in India, motivated by similar work done in Ghosh et al (2016), which studied the probability distribution of rainfall in multiple cities in Bangladesh. We have determined the best-fit probability distribution for the monthly precipitation data spanning 100 years of data from 1901 to 2002, for multiple stations located all over India, such as Gandhinagar, Guntur, Hyderabad, Jaipur, Kohima, Kurnool, and Patna. To fit the observed data, we considered the Fisher, Gamma, Gumbel, Inverse Gaussian, Normal, Weibull, Student-t, Beta, and Generalized Extreme Value distributions. The efficacy of the fits for these distributions are evaluated using four empirical non-parametric goodness-of-fit tests namely Kolmogorov-Smirnov (KS), Anderson-Darling (AD), Chi-Square, Akaike information criterion(AIC) and Bayesian Information criterion (BIC). Finally, the best-fit distribution using each of these tests are reported for the various cities.

Modified Kolmogorov- Smirnov (KS), Anderson-Darling (AD), Cramer-von Mises (CV), Kupier (V), and Watson (W) goodness-of-fit tests are generated for the inverse Gaussian distribution with unknown parameters. The inverse Gaussian parameters are estimated by maximum likelihood estimation. A Monte Carlo simulation of 50,000 repetitions is used to generate critical values for sample sizes of 5 through 50 with an increment of five, sample sizes of 60 through 100 with an increment of 10, and 24 different values of the inverse Gaussian shape parameter. A 50,000-repetition Monte Carlo power study is carried out using data with sample sizes of 5 through 100 from five alternate distributions for the five EDF tests for significance levels of 0.01,0.05,0.10, 0.15, and 0.20. For sequential tests, power studies are performed for the significance levels produced by combining two EDF tests. Power studies corresponding two both cases are presented in tables and graphs. The power studies showed that the tests arc excellent in discriminating between the inverse Gaussian and distributions such as the gamma, exponential and uniform that are very different in shape. However, they are relatively unable to discriminate between the inverse Gaussian distribution and distributions that are similar in shape such as the lognormal and certain Weibull distributions with shape similar to the particular inverse Gaussian. The AD test has the highest power in most cases studied. A functional relationship is identified between the modified KS, AD, CV, V, and W test statistics, sample size, and the inverse Gaussian shape parameter. The critical values are found to be a non-linear function of the shape parameters and sample sizes for the significance levels of 0.01, 0.05, 0.10, 0.15, and 0.20.