Devil in the details: how can we avoid potential pitfalls of CATS regression when our data do not follow a Poisson distribution?

Background Community assembly by trait selection (CATS) allows for the detection of environmental filtering and estimation of the relative role of local and regional (meta-community-level) effects on community composition from trait and abundance data without using environmental data. It has been shown that Poisson regression of abundances against trait data results in the same parameter estimates. Abundance data do not necessarily follow a Poisson distribution, and in these cases, other generalized linear models should be fitted to obtain unbiased parameter estimates. Aims This paper discusses how the original algorithm for calculating the relative role of local and regional effects has to be modified if Poisson model is not appropriate. Results It can be shown that the use of the logarithm of regional relative abundances as an offset is appropriate only if a log-link function is applied. Otherwise, the link function should be applied to the product of local total abundance and regional relative abundances. Since this product may be outside the domain of the link function, the use of log-link is recommended, even if it is not the canonical link. An algorithm is also suggested for calculating the offset when data are zero-inflated. The relative role of local and regional effects is measured by Kullback-Leibler R2. The formula for this measure presented by Shipley (2014) is valid only if the abundances follow a Poisson distribution. Otherwise, slightly different formulas have to be applied. Beyond theoretical considerations, the proposed refinements are illustrated by numerical examples. CATS regression could be a useful tool for community ecologists, but it has to be slightly modified when abundance data do not follow a Poisson distribution. This paper gives detailed instructions on the necessary refinement.

Climatological study of the cyclonic storms crossing the east coast of India

Us ~n ~ Poisson distribution the probabil.ity of cyclonic storms crossing each latitude stripon the cast coast of India In a month In a random to-year period l'i com puted and presented in the raper. v ariouscharacteristics of the cyclonic systems such as average speed of movement s, average life spa n and the averagedistan ce travelled alon gwith the coefficient s uf variation before and after crossing the coast are examined anddiscussed here.

Active single cell encapsulation using SAW overcoming the limitations of Poisson distribution

We demonstrate the use of an acoustic device to actively encapsulate single red blood cells into individual droplets in a T-junction. We compare the active encapsulation with the passive encapsulation...

ANALISIS METODE BAYESIAN PADA KINERJA SISTEM ANTREAN INSTALASI RAWAT JALAN RSUP DR. KARIADI (Studi Kasus: Poliklinik Mata, Poliklinik THT, Laboratorium, dan Pendaftaran)

Indonesian people’s awareness of the importance of health has increased significantly so that it has a positive impact on the development of the health sector in Indonesia. The largest service facility in Central Java Province is RSUP Dr. Kariadi. The number of patients who came for an examination at Dr. Kariadi’s arrival rate is unpredictable. This can cause the service system to be busy and result in queues. The purpose of this study was to find out how the service system in Dr. Kariadi especially eye polyclinic, ENT polyclinic, laboratory, and registration. Queue theory has random arrivals and services. Bayesian method is used to analyze the queue system, that has been running for a long time by combining the prior and likelihood distribution of samples. Prior distribution is obtained from previous research, namely the Poisson distribution. Meanwhile, the likelihood of the sample obtained from the current study is the Poisson distribution and the Negative Binomial distribution. The resulting queue models for the eye polyclinic are (GAMM/BETA/4):(GD/∞/∞), ENT polyclinic (GAMM/GAMM/2):(GD/∞/∞), laboratory (GAMM/GAMM/4):(GD/∞/∞), and registration (GAMM/GAMM/3):(GD/∞/∞). Based on the results of the study, it was found that the patient care system at the eye polyclinic, ENT polyclinic, laboratory, and registration met steady state condition, meaning that the service system was running well. The value of the unemployment rate at the eye polyclinic is 96,36%; ENT polyclinic 31,86%; laboratory 34,87% and registration 32.85%. Thus, at the eye polyclinic, the unemployment rate is greater than the busy level. Meanwhile, in ENT polyclinics, laboratories, and registration is the opposite occurs.

Poisson distribution and process as a well-fitting pattern for counting variables in biologic models

One of the major criticisms directed to basic research on high dilution effects is the lack of a steady statistical approach; therefore, it seems crucial to fix some milestones in statistical analysis of this kind of experimentation. Since plant research in homeopathy has been recently developed and one of the mostly used models is based on in vitro seed germination, here we propose a statistical approach focused on the Poisson distribution, that satisfactorily fits the number of non-germinated seeds. Poisson distribution is a discrete-valued model often used in statistics when representing the number X of specific events (telephone calls, industrial machine failures, genetic mutations etc.) that occur in a fixed period of time, supposing that instant probability of occurrence of such events is constant. If we denote with λ the average number of events that occur within the fixed period, the probability of observing exactly k events is: P(k) = e-λ λk /k! , k = 0, 1,2,… This distribution is commonly used when dealing with rare effects, in the sense that it has to be almost impossible to have two events at the same time. Poisson distribution is the basic model of the socalled Poisson process, which is a counting process N(t), where t is a time parameter, having these properties: - The process starts with zero: N(0) = 0; - The increments are independent; - The number of events that occur in a period of time d(t) follows a Poisson distribution with parameter proportional to d(t); - The waiting time, i.e. the time between an event and another one, follows and exponential distribution. In a series of experiments performed by our research group ([1], [2]., [3], [4]) we tried to apply this distribution to the number X of non-germinated seeds out of a fixed number N* of seeds in a Petri dish (usually N* = 33 or N* = 36). The goodness-of-fit was checked by different tests (Kolmogorov distance and chi-squared), as well as with the Poissonness plot proposed by Hoaglin [5]. The goodness-of-fit of Poisson distribution allows to use specific tests, like the global Poisson test (based on a chi-squared statistics) and the comparison of two Poisson parameters, based on the statistic z = X1–X2 / (X1+X2)1/2 which is, for large samples (at least 20 observations) approximately standard normally distributed. A very clear review of these tests based on Poisson distribution is given in [6]. This good fit of Poisson distribution suggests that the whole process of germination of wheat seeds may be considered as a non-homogeneous Poisson process, where the germination rate is not constant but changes over time. Keywords: Poisson process, counting variable, goodness-of-fit, wheat germination References [1] L.Betti, M.Brizzi, D.Nani, M.Peruzzi. A pilot statistical study with homeopathic potencies of Arsenicum Album in wheat germination as a simple model. British Homeopathic Journal; 83: 195-201. [2] M.Brizzi, L.Betti (1999), Using statistics for evaluating the effectiveness of homeopathy. Analysis of a large collection of data from simple plant models. III Congresso Nazionale della SIB (SocietàItaliana di Biometria) di Roma, Abstract Book, 74-76. [3] M.Brizzi, D.Nani, L.Betti, M.Peruzzi. Statistical analysis of the effect of high dilutions of Arsenic in a large dataset from a wheat germination model. British Homeopathic Journal, 2000;, 89, 63-67. [4] M.Brizzi, L.Betti (2010), Statistical tools for alternative research in plant experiments. “Metodološki Zvezki – Advances in Methodology and Statistics”, 7, 59-71. [5] D.C.Hoaglin (1980), A Poissonness plot. “The American Statistician”, 34, 146-149. [6] L.Sachs (1984) Applied statistics. A handbook of techniques. Springer Verlag, 186-189.

Alpha Power Extended Inverse Weibull Poisson Distribution: Properties, Inference, and Applications to lifetime data

In this paper, a new four-parameter extended inverse Weibull distribution called Alpha power Extended Inverse Weibull Poisson distribution is introduced using the alpha power Poisson generator. This method adds two shape parameters to a baseline distribution thereby increasing its flexibility and applicability in modeling lifetime data. We study the structural properties of the new distribution such as the mean, variance, quantile function, median, ordinary and incomplete moments, reliability analysis, Lorenz and Bonferroni curves, Renyi entropy, mean waiting time, mean residual life, and order statistics. We use the method of maximum likelihood technique for estimating the model parameters of Alpha power extended inverse Weibull distribution and the corresponding confidence intervals are obtained. The simulation method is carried out to evaluate the performance of the maximum likelihood estimate in terms of their Absolute Bias and Mean Square Error using simulated data. Two lifetime data sets are presented to demonstrate the applicability of the new model and it is found that the new model has superior modeling power when compare to Inverse Weibull distribution, Alpha Power Poisson inverse exponential distribution, Alpha Power Extended Inverse Weibull distribution, and Alpha Power Extended Inverse Exponential distribution.