Evidential Estimation of an Uncertain Mixed Exponential Distribution under Progressive Censoring

In this paper, the evidential estimation method for the parameters of the mixed exponential distribution is considered when a sample is obtained from Type-II progressively censored data. Different from the traditional statistical inference methods for censored data from mixture models, here we consider a very general form where there is some uncertain information about the sub-class labels of units. The partially specified label information, as well as the censored data are represented in a united frame by mass functions within the theory of belief functions. Following that, the evidential likelihood function is derived based on the completely observed failures and the uncertain information included in the data. Then, the optimization method using the evidential expectation maximization algorithm (E2M) is introduced. A general form of the maximal likelihood estimates (MLEs) in the sense of the evidential likelihood, named maximal evidential likelihood estimates (MELEs), can be obtained. Finally, some Monte Carlo simulations are conducted. The results show that the proposed estimation method can incorporate more information than traditional EM algorithms, and this confirms the interest in using uncertain labels for the censored data from finite mixture models.

PENENTUAN HARGA PREMI ASURANSI PERTANIAN BERBASIS INDEKS CURAH HUJAN DENGAN MENGGUNAKAN METODE PEMBANGKIT DISTRIBUSI EKSPONENSIAL CAMPURAN

Agricultural insurance is an insurance in agriculture sector that is relatively newly introduced in Indonesia. Agricultural insurance based on rainfall index is one of the risk management tool to keep farmers in case of crop failure. This study aims to determine the steps in determining the value of rainfall index on agricultural insurance and calculate the value of agricultural insurance premiums based on simulated rainfall index by Stochastic weather generator with mixed exponential distribution. The results of this study provide value if the amount of rainfall 103,71 mm so that the amount of premium payments equal to Rp19.016, and if the rainfall is high 128.35 mm then the amount of premium payment equal to Rp1.088.000.

TROPICAL DAILY RAINFALL AMOUNT MODELLING USING MARKOV CHAIN-MIXED EXPONENTIAL (MCME)

This study is concerned with the development of a stochastic rainfall model that can generate many sequences of synthetic daily rainfall series with the similar properties as those of the observed. The proposed model is Markov chain-mixed exponential (MCME). This model is based on a combination of rainfall occurrence (represented by the first-order two-state Markov chain) and the distribution of rainfall amounts on wet days (described by the mixed exponential distribution). The feasibility of the MCME model is assessed using daily rainfall data from four rainfall stations (station S02, S05, S07 and S11) in Johor, Malaysia. For all the rainfall stations, it was found that the proposed MCME model was able to describe adequately rainfall occurrences and amounts. Various statistical and physical properties of the daily rainfall processes also considered. However, the validation results show that the models’ predictive ability was not as accurate as their descriptive ability. The model was found to have fairly well ability in predicting the daily rainfall process at station S02, S05 and S07. Nonetheless, it was able to predict the daily rainfall process at station S11 accurately.

Bayesian Estimations of Mixed Exponential Distribution with Type-I Censored Data

Mixed exponential distribution is a very important statistical model in life data analysis. In this paper, we give Bayesian estimations of mixed exponential distribution with Type-Ⅰ censored data by using conjugate prior distribution based on square loss function. And we prove that the Bayesian estimations are admissible.

Fitting The Best–Fit Distribution For The Hourly Rainfall Amount In The Wilayah Persekutuan

Dalam mengenal pasti model yang terbaik untuk mewakili taburan jumlah hujan bagi data selang masa satu jam di 12 stesen di Wilayah Persekutuan empat taburan digunakan iaitu Taburan Eksponen, Gamma, Weibull dan Gabungan Eksponen. Parameter–parameter dianggar menggunakan kaedah kebolehjadian maksimum. Model yang terbaik dipilih berdasarkan nilai minimum yang diperolehi daripada ujian–ujian kebagusan penyuaian yang digunakan dalam kajian ini. Ujian ini dipertahankan lagi dengan plot kebarangkalian dilampaui. Taburan Gabungan Eksponen di dapati paling baik untuk mewakili taburan jumlah hujan dalam selang masa satu jam. Daripada anggaran parameter bagi taburan Gabungan Eksponen ini, boleh diterjemah bahawa jumlah hujan tertinggi yang direkodkan diperolehi daripada hujan yang dikategorikan sebagai hujan lebat, walaupun hujan renyai–renyai berlaku lebih kerap. Kata kunci: Jumlah hujan dalam selang masa sejam, ujian kebagusan penyuaian, kebolehjadian maksimum In determining the best–fit model for the hourly rainfall amounts for the twelve stations in the Wilayah Persekutuan, four distributions namely, the Exponential, Gamma, Weibull and Mixed–Exponential were used. Parameters for each distribution were estimated using the maximum likelihood method. The best–fit model was chosen based upon the minimum error produced by the goodness–offit tests used in this study. The tests were justified further by the exceedance probability plot. The Mixed–Exponential was found to be the most appropriate distribution in describing the hourly rainfall amounts. From the parameter estimates for the Mixed–Exponential distribution, it could be implied that most of the hourly rainfall amount recorded were received from the heavy rainfall even though there was a high occurrences of light rainfall. Key words: Hourly rainfall amount, goodness-of-fit test, exceedance probability, maximum likelihood

Dynamic Simulation of 3D Fluid Field for Four-Wing Synchronous Mixer Rotor and Four-Wing Asynchronous Mixer Rotor

The physical, mathematical and finite element models for the four-wing synchronous rotors and four-wing asynchronous rotors in internal mixer were established in this paper. By comparative analysis of the two types of processes involved in mixing process the pressure field, the velocity field and the concentration field, the viscosity field and the mixed exponential distribution on its 3D fluid field dynamic simulation were computed by the polyflow software. The results showed that the four-wing synchronous rotors were better than the four-wing asynchronous rotors in a number of performance parameters.

Regional frequency analysis of extreme storm surges along the French coast

A good knowledge of extreme storm surges is necessary to ensure protection against flood. In this paper we introduce a methodology to determine time series of skew surges in France as well as a statistical approach for estimating extreme storm surges. With the aim to cope with the outlier issue in surge series, a regional frequency analysis has been carried out for the surges along the Atlantic coast and the Channel coast. This methodology is not the current approach used to estimate extreme surges in France. First results showed that the extreme events identified as outliers in at-site analyses do not appear to be outliers any more in the regional empirical distribution. Indeed the regional distribution presents a curve to the top with these extreme events that a mixed exponential distribution seems to recreate. Thus, the regional approach appears to be more reliable for some sites than at-site analyses. A fast comparison at a given site showed surge estimates with the regional approach and a mixed exponential distribution are higher than surge estimates with an at-site fitting. In the case of Brest, the 1000-yr return surge is 167 cm in height with the regional approach instead of 126 cm with an at-site analysis.

A Mixed Exponential Distribution Model for Retrieving Ground Flash Fraction from Satellite Lightning Imager Data

A Bayesian inversion method is introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employs a constrained mixed exponential distribution model to describe the lightning optical measurements. Because the method also retrieves certain population statistics of ground and cloud flash optical properties, the method can be applied to an arbitrary geographical region, including those regions where the lightning optical statistics either are not known or are difficult to obtain. The approach is tested by performing simulated retrievals, and retrieval error statistics are provided. A first-attempt retrieval of the global geographical distribution of ground flash fraction is obtained using the 5-yr Optical Transient Detector (OTD) dataset; the spatially averaged ground flash fraction over the global-scale domain studied was 0.151 with a standard deviation of 0.081. The ability to retrieve ground flash fraction has important benefits to the atmospheric chemistry community. For example, using the method to partition the existing OTD/Lightning Imaging Sensor (LIS) satellite global lightning climatology into separate ground and cloud flash climatologies would improve estimates of regional and global lightning nitrogen oxides (NOx) production; this, in turn, would improve both regional air quality and global chemistry/climate model predictions.