#  Look at the two spurious continuous
#  probability distributions given on the web page,
#  namely the Apfelton and the Blumenkopf 
#  distributions.
#
#  We will just repeat the kind of questions that
#  we saw in the binomial distribution.
#

############################################
#   Using the table, find
#For the Apfelton distribution
#  P(X < -0.47 ) = 
#  P(X <= 2.38 ) = 
#  P(X < 3.3765) =
#  P( X > 2.24 ) =
#  P( X > -1.39 ) =
#  P( -0.62 < X < 1.26 ) =
#  P( X < 0.34  or X>0.98 ) =
######################################

######################################
# now do the same using the papfelton() function
source("../apfelton.R")
#  P(X < -0.47 ) = 
papfelton( -0.47 )

#  P(X <= 2.38 ) = 
papfelton( 2.38 )

#  P(X < 3.3765) =
papfelton( 3.3765 )

#  P( X > 2.24 ) =
1 - papfelton( 2.24 ) # Is one approach
papfelton( 2.24, lower.tail=FALSE )  # another way

#  P( X > -1.39 ) =
1 - papfelton( -1.39 ) # Is one approach
papfelton( -1.39, lower.tail=FALSE )  # another way

#  P( -0.62 < X < 1.26 ) =
papfelton(1.26) - papfelton(-0.62)

#  P( X < 0.34  or X>0.98 ) = 
papfelton(0.34) + (1-papfelton(0.98))  # is one way
papfelton(0.34) + 
    papfelton( 0.98, lower.tail=FALSE)# is another way

#######################################
##  go back to the table and use it to solve:
#
#  find the y value such that
#      P(X < y ) = 0.2345    y=
#      P(X < y ) = 0.7608    y=
#      P(X > y ) = 0.3512    y=
#      P(X > y ) = 0.9199    y=
#      P(X < y ) = 0.5981    y=
######################################

######################################
# now do the same using the qapfelton() function
#      P(X < y ) = 0.2345    y=
qapfelton( 0.2345 )

#      P(X < y ) = 0.7608    y=
qapfelton( 0.7608 )

#      P(X > y ) = 0.3512    y=
qapfelton( 1 - 0.3512 )  # is one way
qapfelton( 0.3512, lower.tail=FALSE ) # is another way

#      P(X > y ) = 0.9199    y=
qapfelton( 1 - 0.9199 )  # is one way
qapfelton( 0.9199, lower.tail=FALSE ) # is another way

#      P(X < y ) = 0.5981    y=
qapfelton( 0.5981 )

#################################################
####   Switch to the Blumenkopf distribution.
####   Remember that the Blumenkopf is a 
####   symmetric distribution, so the are some
####   more questions that we might ask
############################################
#   Using the table, find
#For the Blumenkopf distribution
#  P(X < -0.47 ) = 
#  P(X <= 2.38 ) = 
#  P(X < 3.3765) =
#  P( X > 2.24 ) =
#  P( X > -1.39 ) =
#  P( -0.62 < X < 1.26 ) =
#  P( X < 0.34  or X>0.98 ) =
######################################

######################################
# now do the same using the pblumenkopf() function
source("../blumenkopf.R")
#  P(X < -0.47 ) = 
pblumenkopf( -0.47 )

#  P(X <= 2.38 ) = 
pblumenkopf( 2.38 )

#  P(X < 3.3765) =
pblumenkopf( 3.3765 )

#  P( X > 2.24 ) =
1 - pblumenkopf( 2.24 ) # Is one approach
pblumenkopf( 2.24, lower.tail=FALSE )  # another way
#     and, because it is symmetric we could do
pblumenkopf( -2.24)

#  P( X > -1.39 ) =
1 - pblumenkopf( -1.39 ) # Is one approach
pblumenkopf( -1.39, lower.tail=FALSE )  # another way
#     and, because it is symmetric we could do
pblumenkopf( 1.39)

#  P( -0.62 < X < 1.26 ) =
pblumenkopf(1.26) - pblumenkopf(-0.62)

#  P( X < 0.34  or X>0.98 ) = 
pblumenkopf(0.34) + (1-pblumenkopf(0.98))  # is one way
pblumenkopf(0.34) + 
  pblumenkopf( 0.98, lower.tail=FALSE)# is another way

#######################################
##  go back to the table and use it to solve:
#
#  find the y value such that
#      P(X < y ) = 0.2332    y=
#      P(X < y ) = 0.7614    y=
#      P(X > y ) = 0.3600    y=
#      P(X > y ) = 0.9182    y=
#      P(X < y ) = 0.5981    y=
#         because Blumenkopf is symmetric
#      P( X < -y or X > y) = 0.2538   y=
#         because Blumenkopf is symmetric
#      P( -y < X < y) = 0.4610   y=

######################################

######################################
# now do the same using the qblumenkopf() function
#      P(X < y ) = 0.2332    y=
qblumenkopf( 0.2332 )

#      P(X < y ) = 0.7614    y=
qblumenkopf( 0.7614 )

#      P(X > y ) = 0.3600    y=
qblumenkopf( 1 - 0.3600 )  # is one way
qblumenkopf( 0.3600, lower.tail=FALSE ) # is another way

#      P(X > y ) = 0.9182    y=
qblumenkopf( 1 - 0.9182 )  # is one way
qblumenkopf( 0.9182, lower.tail=FALSE ) # is another way

#      P(X < y ) = 0.5981    y=
qblumenkopf( 0.5981 )

#         because Blumenkopf is symmetric
#      P( X < -y or X > y) = 0.2538   y=
qblumenkopf(0.2538/2, lower.tail=FALSE)

#         because Blumenkopf is symmetric
#      P( -y < X < y) = 0.4610   y=
qblumenkopf((1 - 0.4610)/2, lower.tail=FALSE)
    #   but note that
qblumenkopf( (1-0.4610)/2 ) # also works, sort of