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International Journal of Mathematics and Mathematical Sciences
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Table of Contents
Special Issues
International Journal of Mathematics and Mathematical Sciences
/
2009
/
Article
/
Tab 1
/
Research Article
Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior
Table 1
Parameters of the numerical example.
Parameter
Value
𝐽
1
,
2
,
…
,
9
𝜆
(
𝑥
)
[
…
,
3
𝑗
2
𝑥
2
,
…
]
⊤
𝒜
{
0
,
1
,
…
,
𝐽
−
1
}
ℳ
{
𝐽
−
1
}
𝒩
{
𝐽
}
𝑀
(
𝑡
)
∑
𝑖
∈
𝒜
𝑀
𝑖
(
𝑡
)
𝑁
(
𝑡
)
∑
𝑖
∈
ℳ
,
𝑗
∈
𝒩
𝑁
𝑖
𝑗
(
𝑡
)
Θ
(
𝑖
,
𝑗
)
√
e
x
p
(
𝑖
−
7
.
9
)
+
e
x
p
(
7
.
9
−
𝑗
)
Θ
(
𝑖
,
𝑗
)
1
+
1
e
x
p
(
𝑖
+
𝑗
−
5
)
2
𝜃
[
Θ
(
0
,
0
)
Θ
(
0
,
1
)
0
⋯
0
0
⋱
⋱
0
⋮
⋮
0
Θ
(
𝑖
,
𝑖
)
Θ
(
𝑖
,
𝑖
+
1
)
0
0
⋱
⋱
⋱
Θ
(
𝐽
,
𝐽
+
1
)
0
⋯
0
Θ
(
𝐽
,
𝐽
)
]
̂
𝜃
[
Θ
(
0
,
0
)
Θ
(
0
,
1
)
0
⋯
0
0
⋱
⋱
0
⋮
⋮
0
Θ
(
𝑖
,
𝑖
)
Θ
(
𝑖
,
𝑖
+
1
)
0
0
⋱
⋱
⋱
Θ
(
𝐽
,
𝐽
+
1
)
0
⋯
0
Θ
(
𝐽
,
𝐽
)
]
𝜓
𝑑
10
𝜓
𝑚
1000
𝑇
1000