The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

A new method to analyze the subjective visual vertical in patients with bilateral vestibular dysfunction

OBJECTIVE: The aim of this study was to assess the subjective visual vertical in patients with bilateral vestibular dysfunction and to propose a new method to analyze subjective visual vertical data in these patients. METHODS: Static subjective visual vertical tests were performed in 40 subjects split into two groups. Group A consisted of 20 healthy volunteers, and Group B consisted of 20 patients with bilateral vestibular dysfunction. Each patient performed six measurements of the subjective visual vertical test, and the mean values were calculated and analyzed. RESULTS: Analyses of the numerical values of subjective visual vertical deviations (the conventional method of analysis) showed that the mean deviation was 0.326 +/- 1.13 degrees in Group A and 0.301 +/- 1.87 degrees in Group B. However, by analyzing the absolute values of the subjective visual vertical (the new method of analysis proposed), the mean deviation became 1.35 +/- 0.48 degrees in Group A and 2.152 +/- 0.93 degrees in Group B. The difference in subjective visual vertical deviations between groups was statistically significant (p < 0.05) only when the absolute values and the range of deviations were considered. CONCLUSION: An analysis of the absolute values of the subjective visual vertical more accurately reflected the visual vertical misperception in patients with bilateral vestibular dysfunction.

General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883-898], proposed a new generalized distribution (denoted here with the prefix 'Kw-G'(Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-Gdensity function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155-161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279-285] and Kw-Flexible Weibull [M. Bebbington, C. D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719-726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Renyi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.

Nerve fiber layer in glaucomatous hemifield loss: a case-control study with time- and spectral-domain optical coherence tomography

Purpose: To evaluate the retinal nerve fiber layer measurements with time-domain (TD) and spectral-domain (SD) optical coherence tomography (OCT), and to test the diagnostic ability of both technologies in glaucomatous patients with asymmetric visual hemifield loss. Methods: 36 patients with primary open-angle glaucoma with visual field loss in one hemifield (affected) and absent loss in the other (non-affected), and 36 age-matched healthy controls had the study eye imaged with Stratus-OCT (Carl Zeiss Meditec Inc., Dublin, California, USA) and 3 D OCT-1000 (Topcon, Tokyo, Japan). Peripapillary retinal nerve fiber layer measurements and normative classification were recorded. Total deviation values were averaged in each hemifield (hemifield mean deviation) for each subject. Visual field and retinal nerve fiber layer "asymmetry indexes" were calculated as the ratio between affected versus non-affected hemifields and corresponding hemiretinas. Results: Retinal nerve fiber layer measurements in non-affected hemifields (mean [SD] 87.0 [17.1] mu m and 84.3 [20.2] mu m, for TD and SD-OCT, respectively) were thinner than in controls (119.0 [12.2] mu m and 117.0 [17.7] mu m, P<0.001). The optical coherence tomography normative database classified 42% and 67% of hemiretinas corresponding to non-affected hemifields as abnormal in TD and SD-OCT, respectively (P=0.01). Retinal nerve fiber layer measurements were consistently thicker with TD compared to SD-OCT. Retinal nerve fiber layer thickness asymmetry index was similar in TD (0.76 [0.17]) and SD-OCT (0.79 [0.12]) and significantly greater than the visual field asymmetry index (0.36 [0.20], P<0.001). Conclusions: Normal hemifields of glaucoma patients had thinner retinal nerve fiber layer than healthy eyes, as measured by TD and SD-OCT. Retinal nerve fiber layer measurements were thicker with TD than SD-OCT. SD-OCT detected abnormal retinal nerve fiber layer thickness more often than TD-OCT.

Comparison of Visual Acuity and Automated Perimetry Findings in Patients With Neuromyelitis Optica or Multiple Sclerosis After Single or Multiple Attacks of Optic Neuritis

Objective: To review the clinical characteristics of patients with neuromyelitis optica (NMO) and to compare their visual outcome with those of patients with optic neuritis (ON) and multiple sclerosis (MS). Methods: Thirty-three patients with NMO underwent neuro-ophthalmic evaluation, including automated perimetry along with 30 patients with MS. Visual function in both groups was compared overall and specifically for eyes after a single episode of ON. Results: Visual function and average visual field (VF) mean deviation were significantly worse in eyes of patients with NMO. After a single episode of ON, the VF was normal in only 2 of 36 eyes of patients with NMO compared to 17 of 35 eyes with MS (P < 0.001). The statistical analysis indicated that after a single episode of ON, the odds ratio for having NMO was 6.0 (confidence interval [CI]: 1.6-21.9) when VF mean deviation was worse than -20.0 dB while the odds ratio for having MS was 16.0 (CI: 3.6-68.7) when better than -3.0 dB. Conclusion: Visual outcome was significantly worse in NMO than in MS. After a single episode of ON, suspicion of NMO should be raised in the presence of severe residual VF deficit with automated perimetry and lowered in the case of complete VF recovery.

Rates of Change in the Visual Field and Optic Disc in Patients with Distinct Patterns of Glaucomatous Optic Disc Damage

Purpose: To investigate the rate of visual field and optic disc change in patients with distinct patterns of glaucomatous optic disc damage. Design: Prospective longitudinal study. Participants: A total of 131 patients with open-angle glaucoma with focal (n = 45), diffuse (n = 42), and sclerotic (n = 44) optic disc damage. Methods: Patients were examined every 4 months with standard automated perimetry (SAP, SITA Standard, 24-2 test, Humphrey Field Analyzer, Carl Zeiss Meditec, Dublin, CA) and confocal scanning laser tomography (CSLT, Heidelberg Retina Tomograph, Heidelberg Engineering GmbH, Heidelberg, Germany) for a period of 4 years. During this time, patients were treated according to a predefined protocol to achieve a target intraocular pressure (IOP). Rates of change were estimated by robust linear regression of visual field mean deviation (MD) and global optic disc neuroretinal rim area with follow-up time. Main Outcome Measures: Rates of change in MD and rim area. Results: Rates of visual field change in patients with focal optic disc damage (mean -0.34, standard deviation [SD] 0.69 dB/year) were faster than in patients with sclerotic (mean - 0.14, SD 0.77 dB/year) and diffuse (mean + 0.01, SD 0.37 dB/year) optic disc damage (P = 0.003, Kruskal-Wallis). Rates of optic disc change in patients with focal optic disc damage (mean - 11.70, SD 25.5 x 10(-3) mm(2)/year) were faster than in patients with diffuse (mean -9.16, SD 14.9 x 10(-3) mm(2)/year) and sclerotic (mean -0.45, SD 20.6 x 10(-3) mm(2)/year) optic disc damage, although the differences were not statistically significant (P = 0.11). Absolute IOP reduction from untreated levels was similar among the groups (P = 0.59). Conclusions: Patients with focal optic disc damage had faster rates of visual field change and a tendency toward faster rates of optic disc deterioration when compared with patients with diffuse and sclerotic optic disc damage, despite similar IOP reductions during follow-up. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references. Ophthalmology 2012; 119: 294-303 (C) 2012 by the American Academy of Ophthalmology.

Effect of aspherical and yellow tinted intraocular lens on blue-on-yellow perimetry

PURPOSE: To investigate the possible effect of aspherical or yellow tinted intraocular lens (IOL) on contrast sensitivity and blue-on-yellow perimetry. METHODS: This prospective randomized bilateral double-masked clinical study included 52 patients with visually significant bilateral cataracts divided in two groups; 25 patients (50 eyes) received aspherical intraocular lens in one eye and spherical intraocular lens in the fellow eye; and 27 patients (54 eyes) received ultraviolet and blue light filter (yellow tinted) IOL implantation in one eye and acrylic ultraviolet filter IOL in the fellow eye. The primary outcome measures were contrast sensitivity and blue-on-yellow perimetry values (mean deviation [MD] and pattern standard deviation [PSD]) investigated two years after surgery. The results were compared intra-individually. RESULTS: There was a statistically significant between-group (aspherical and spherical intraocular lens) difference in contrast sensitivity under photopic conditions at 12 cycles per degree and under mesopic conditions at all spatial frequencies. There were no between-group significant differences (yellow tinted and clear intraocular lens) under photopic or mesopic conditions. There was no statistically significant difference between all intraocular lens in MD or PSD. CONCLUSION: Contrast sensitivity was better under mesopic conditions with aspherical intraocular lens. Blue-on-yellow perimetry did not appear to be affected by aspherical or yellow tinted intraocular lens. Further studies with a larger sample should be carried out to confirm or not that hypotheses.