Four statistical models for wet-spell analysis

Wet-spell analysis is an important part of rainfall analysis. The distribution of the length of wet-spells provides useful information on the temporal distribution of rainfall. This distribution has traditionally been modelled through different probability distributions. Here we compare four such models, namely, Cochran's model, truncated Poisson distribution, truncated negative binomial distribution, and logarithmic series distribution. These comparisons are accomplished with help of application to five rainguage stations in India.

On Methods of Estimation for Generalized Logarithmic Series Distribution and Its Application to Counts of Red Mites on Apple Leaves

The Generalized Logarithmic Series Distribution (GLSD) adds an extra parameter to the usual logarithmic series distribution and was introduced by Jain and Gupta (1973). This distribution has found applications in various fields. The estimation of parameters of generalized logarithmic series distribution was studied by the methods of maximum likelihood, moments, minimum chi square and weighted discrepancies. The GLSD was fitted to counts of red mites on apple leaves and it was observed that all the estimation techniques perform well in estimating the parameters of generalized logarithmic series distribution but with varying degree of non-significance.

Forecasting of Cotton Production in India using Advanced Time Series Models

Reliable and timely estimates of cotton production are important providing useful inputs to policymakers for proper foresighted and informed planning. So an attempt was made to forecast the production of cotton at all India level using a time series model. The annual data on production of cotton for the period 1951-52 to 2018-19 was processed. The data were transformed into logarithmic series to stabilize the variance of the series. The stationarity of the data was checked with the help of the Augmented Dickey-Fuller and Phillips-Perron tests. The results of ADF and PP tests confirmed the cotton production series was non-stationary at level, so stationarity in the data was brought by differencing the data series at a first lag. The pattern present in ACF and PACF and results of SCAN and ESACF provided guideline to select the order of non-seasonal ARIMA model. The best fit ARIMA model (ARIMA: 3 1 1) was selected based on AIC criteria and residual diagnostic. The performance of the model was judged based on the MAPE value. The out of sample forecast of cotton production at all India level was carried out for the period 2019-20 to 2021-22. The forecasted values indicated a slight increase in the production of cotton compared to 2018-19.

Out-of-plane buckling in two-dimensional glass drawing

We derive a mathematical model for the drawing of a two-dimensional thin sheet of viscous fluid in the direction of gravity. If the gravitational field is sufficiently strong, then a portion of the sheet experiences a compressive stress and is thus unstable to transverse buckling. We analyse the dependence of the instability and the subsequent evolution on the process parameters, and the mutual coupling between the weakly nonlinear buckling and the stress profile in the sheet. Over long time scales, the sheet centreline ultimately adopts a universal profile, with the bulk of the sheet under tension and a single large bulge caused by a small compressive region near the bottom, and we derive a canonical inner problem that describes this behaviour. The large-time analysis involves a logarithmic asymptotic expansion, and we devise a hybrid asymptotic–numerical scheme that effectively sums the logarithmic series.

On Finite Part Integrals and Hadamard-Type Fractional Derivatives

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.