The value of Bitcoin is proportional to Bitcoin Halving (reward).
(The lower the reward, the higher the price)
The Pi Cycle indicators is composed of the 111 day moving average (111SMA) and a 2x multiple of the 350 day moving average (350SMA x 2) of Bitcoin's price. This metric shows when BTC becomes significantly overheated (the shorter MA reaches the levels of the larger MA), and has historically been a good indicator for cycle tops.
an exponential distribution,
fτ(t) = αe
−αt
where α = 1/t0 = 1/E[T]. If the miner starts mining at t = 0,
and if we denote T1 the time needed to mine a first block,
then T2, . . . ,Tn the inter-block mining times of successive
blocks, then the Markov property shows that the random variables T1,T2, . . . ,Tn are independent and are all identically
distributed following the same exponential law. Therefore,
the time needed to discover n blocks is
Sn = T1 + T2 + . . . + Tn .
The random variable Sn follows the n-convolution of the exponential distribution and, as is well known, this gives a Gamma
distribution with parameters (n, α),
fSn
(t) =
α
n
(n − 1)!
t
n−1
e
−αt
with cumulative distribution
FSn
(t) =
Z t
0
fSn
(u)du = 1 − e
−αt Xn−1
k=0
(αt)
k
k!
.
From this we conclude that if N(t) is the process counting the
number of blocks validated at time t > 0, N(t) = max{n ≥
0; Sn < t}, then we have
P[N(t) = n] = FSn
(t) − FSn+1
(t) =
(αt)
n
n!
e
−αt
,
and N(t) follows a Poisson law with mean value αt. This result is classical, and the mathematics of Bitcoin mining, as
well as other crypto-currencies with validation based on proof
of work, are Poisson distributions.
https://prnt.sc/lxfO24fLqO3d
