Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Direct effect of PGF2 alpha pulses on PRL pulses, based on inhibition of PRL or PGF2 alpha secretion in heifers

The relationships between PRL and PGF(2 alpha) and their effect on luteolysis were studied. Heifers were treated with a dopamine-receptor agonist (bromocriptine; Bc) and a Cox-1 and -2 inhibitor (flunixin meglumine [FM]) to inhibit PRL and PGF(2 alpha), respectively. The Bc was given (Hour 0) when ongoing luteolysis was indicated by a 12.5% reduction in CL area (cm(2)) from the area on Day 14 postovulation, and FM was given at Hours 0, 4, and 8. Blood samples were collected every 8-h beginning on Day 14 until Hour 48 and hourly for Hours 0 to 12. Three groups of heifers in ongoing luteolysis were used: control (n = 7), Bc (n = 7), and FM (n = 4). Treatment with Bc decreased (P < 0.003) the PRL concentrations averaged over Hours 1 to 12. During the greatest decrease in PRL (Hours 2-6), LH concentrations were increased. Progesterone concentrations averaged over hours were greater (P < 0.05) in the Bc group than in the controls. In the FM group, no PGFM pulses were detected, and PRL concentrations were reduced. Concentrations of PGFM were not reduced in the Bc group, despite the reduction in PRL. Results supported the hypothesis that a decrease (12.5%) in CL area (cm(2)) is more efficient in targeting ongoing luteolysis (63%) than using any day from Days 14 to >= 19 (efficiency/day, 10-24%). The hypothesis that PRL has a role in luteolysis was supported but was confounded by the known positive effect of LH on progesterone. The hypothesis was supported that the synchrony of PGFM and PRL pulses represents a positive effect of PGF(2 alpha), on PRL, rather than an effect of PRL on PGF(2 alpha). (C) 2012 Elsevier Inc. All rights reserved.

Unilateral ablation of follicles >= 4 mm leads to compensatory follicle response from the contralateral ovary in heifers

In each of two experiments, heifers were assigned to a control group and a unilaterally ablated (UA) group (n = 6/group). In the UA group, follicles >= 4 mm in the left ovary were ablated by transvaginal ultrasound-guided technique at Hour 0 (8:00 AM) on the day of ovulation. Follicles in the CL-bearing right ovary remained intact. In Experiment 1, ablations continued until the next ovulation, and new follicles emerged in the right ovary in 9 of 14 (64%) waves. The number of follicles/wave (combined, 6.4 +/- 0.4) did not differ between groups. In Experiment 2, follicles were counted at Hours 0, 4, 8, 12, and 24; the resistance index (RI) for blood flow in the ovarian pedicle was determined at Hours 0 and 12; and blood samples were collected every hour from Hours 0 to 12 and Hour 24. An increase (P < 0.05) in the number of follicles in the follicle-intact ovary began at Hour 4 with complete compensation by Hour 24. Concentrations of FSH did not change between Hours 0 and 24 in the UA group but decreased (P < 0.05) in the controls by Hour 7. At Hour 12, RI to the right ovary approached being lower (P < 0.06) in the UA group than in the control group. Results indicated that unilateral ablation of follicles >= 4 mm led to compensatory follicle response in the follicle-intact ovary, and initially circulatory FSH concentrations were maintained and blood flow to the follicle-intact ovary increased. (c) 2012 Elsevier Inc. All rights reserved.

Temporal relationships of a pulse of prolactin (PRL) to a pulse of a metabolite of PGF2 alpha in mares

Hourly blood samples were collected from 10 mares during 24 h of each of the preluteolytic, luteolytic, and postluteolytic periods. The autocorrelation function of the R program was used to detect pulse rhythmicity, and the intra-assay CV was used to locate and characterize pulses of prolactin (PRL) and a metabolite of prostaglandin F2 alpha (PGFM). Rhythmicity of PRL and PGFM concentrations was detected in 67% and 89% of mares, respectively. Combined for the three periods (no difference among periods), the PRL pulses were 5.2 +/- 0.4 h (mean +/- SEM) at the base, 7.5 +/- 1.5 h between nadirs of adjacent pulses, and 12.3 +/- 1.5 h from peak to peak. The peaks of PRL pulses were greater (P < 0.05) during the luteolytic period (46 +/- 14 ng/mL) and postluteolytic period (52 15 ng/mL) than during the preluteolytic period (17 3 ng/mL). Concentrations of PRL during hours of a PGFM pulse were different (P < 0.003) within the luteolytic period and postluteolytic period and were greatest at the PGFM peak; PRL concentrations during a PGFM pulse were not different during the preluteolytic period. The frequency of the peak of PRL and PGFM pulses occurring at the same hour (synchrony) was greater for the luteolytic period (65%, P < 0.01) and postluteolytic period (50%, P < 0.001) than for the preluteolytic period (17%). This is the first report in mares on characterization and rhythmicity of PRL pulses, synchrony between PRL and PGFM pulses, and greater PRL activity during the luteolytic and postluteolytic periods than during the preluteolytic period. (C) 2012 Elsevier Inc. All rights reserved.

Ovarian and PGF2 alpha responses to stimulation of endogenous PRL pulses during the estrous cycle in mares

The effects of a PRL-stimulating substance (sulpiride) on PRL and PGF2 alpha secretion and on luteal and ovarian follicular dynamics were studied during the estrous cycle in mares. A control group (n = 9) and a sulpiride group (Sp; n = 10) were used. Sulpiride (25 mg) was given every 8 h from Day 13 postovulation to the next ovulation. Repeated sulpiride treatment did not appear to maintain PRL concentrations at 12-h intervals beyond Day 14. Therefore, the hypothesis that a long-term increase in PRL altered luteal and follicular end points was not testable. Hourly samples were collected from the hour of a treatment (Hour 0) to Hour 8 on Day 14. Concentrations of PRL increased to maximum at Hour 4 in the Sp group. The PRL pulses were more prominent (P < 0.008) in the sulpiride group (peak, 19.4 +/- 1.9 ng/mL; mean +/- SEM) than in the controls (11.5 +/- 1.8 ng/mL). Concentrations of a metabolite of PGF2a (PGFM), number, and characteristics of PGFM pulses, and concentrations of progesterone during Hours 0 to 8 were not affected by the increased PRL. A novel observation was that the peak of a PRL pulse occurred at the same hour or 1 h later than the peak of a PGFM pulse in 8 of 8 PGFM pulses in the controls and in 6 of 10 pulses in the Sp group (P < 0.04), indicating that sulpiride interfered with the synchrony between PGFM and PRL pulses. The hypothesis that sulpiride treatment during the equine estrous cycle increases concentrations of PRL and the prominence of PRL pulses was supported. (c) 2012 Elsevier Inc. All rights reserved.